An Egyptian driver waited on Tuesday at the El Auja crossing on the border with Israel. The trickle of trucks that had been going through there has all but stopped, officials and drivers there said.

This normally quiet commercial crossing between Egypt and Israel has been turned into a parking lot of stalled, humanitarian aid, and in the city of El Arish there are even greater quantities of food, clothing and essential supplies, sitting, waiting and baking in the sun. Some supplies are loaded onto dozens of trucks parked on city streets, but much more is stored in the open areas of a local sports stadium, also waiting, also going nowhere. Only medical supplies seem to be getting through to Gaza.

Since the cease-fire, Israel has allowed some humanitarian supplies into Gaza, but the territory is still desperately short of the necessities. Israel closed all the crossings into Gaza on Tuesday after an Israeli soldier was killed in a bombing on the Israeli side of the border. But that changed nothing at this crossing, where the flow has been stalled for days.

Officials and volunteers in Egypt blame the Israelis, saying that even before the passage stalled Israel had allowed supplies to pass through for only 19 hours each week. Israeli officials said that Egypt had not done enough to coordinate the flood of aid coming to Gaza, and that they hoped a system would soon be in place to remedy the problem.

In the meantime, truckloads of humanitarian aid are sitting in Egypt. That includes 13 generators and Amir Abdullah’s trailer full of food.

“All our lunchmeat, it’s all going to go bad,” said Mr. Abdullah, whose tractor-trailer loaded with food and blankets sat in a line outside the stadium in El Arish for 24 hours without moving.

But he is a newcomer to the great humanitarian wait for Gaza.

“We are getting a lot of assistance, but they let very few trucks through,” said Hany Moustafa, who manages the stadium. “We have trucks we loaded up five days ago still sitting here, waiting.”

There has been an outpouring of support for Gazans, mostly from the Arab world, but also from Europe, Venezuela and nongovernmental organizations, officials here said. Medical supplies go straight into Gaza through Egypt’s crossing at Rafah.

But Egypt will not allow anything else to pass through Rafah, insisting that all other aid travel first into Israel and then into Gaza. That is where the bottleneck has occurred. Two of the main problems have been the short window for supplies to pass and Israel’s decision to let few trucks go through, officials and volunteers here said. But another problem has to do with Egypt’s being unprepared to meet strict Israeli packing requirements, which would allow the goods to be passed through security scanners and onto Israeli trucks for delivery to Gaza.

The Egyptians tried to send through trucks carrying bags of flour and sugar, for example, only to have the Israelis send them back. Much has been repacked and reshipped, but some of the returned items are spilled out over the sandy earth at the crossing.

“The trucks get to Auja and they sit,” said Ahmed Oraby, head of the Red Crescent office in El Arish. “Many trucks that left are now coming back. They don’t take anything.”

At the United Nations, John Holmes, an emergency relief coordinator, said the scale of the destruction meant that far more than the current movement of aid was needed urgently. “Enough will always be allowed in for people to exist, but not enough for the conditions for people to live,” Mr. Holmes told reporters.

In recent days, officials and drivers at the crossing said that the trickle of trucks passing through this month had all but stopped. None went on Thursday. Friday and Saturday are days off, so nothing passed. On Sunday, a few trucks went through, aid workers said. Monday, nothing. Tuesday, nothing.

“I have been sitting here for three days, and before that I was in Arish for four days,” said Sayed Ahmed Sorour, seated in the cab of a truck hauling clothing and blankets. “Nobody is telling us anything. Not Egypt. Not Israel. Nobody explains to us why we are stopping here.”

Mr. Sorour’s truck was about 10th in line in front of the gate to enter the border zone. About 30 trucks in all were parked outside the gate, their drivers tired, dirty and frustrated after days of waiting, sleeping in their cabs and killing time.

Inside the gate, parked in the sand near the border with Israel, there were an additional 30 truckloads of flour and sugar and, from the French, the technical gear and bottles of Evian. An Egyptian state security officer, who spoke on the condition of anonymity because of the nature of his work, said there did not seem to be any rational explanation for how the crossing worked. He said he and the other officers simply waited for the Israelis to tell them how many trucks to let in, and they complied.

By 5 p.m., when it was clear that Yasir Hussein was not going to get to deliver his goods, again, he and some other drivers laid down a blanket, warmed some water on a small gas burner and shared small glasses of tea. Mr. Hussein said he was hauling a load of food donated by the Swiss and had been sitting at the gate since Thursday.

“We are not moving, and no one is saying anything,” he said. “We are just trying to help.”

Smoke rises from Israeli missile strikes in Gaza City on Saturday.

After 22 days of war against Hamas, and the deaths of more than 1,200 Palestinians and 13 Israelis, Prime Minister Ehud Olmert insisted that “we have reached all the goals of the war, and beyond.” Speaking to the nation late Saturday night, he said that Hamas had “suffered a major blow” and that if it continued to fire rockets into Israel, “the Israeli Army will regard itself as free to respond with force.”

Hamas, battered but hardly broken, said in Gaza that it would continue fighting so long as Israeli troops occupy Gaza. And Israeli officials say a new flurry of rocket launches, to prove that Hamas is neither cowed nor defeated, is likely for at least a short time.

Heavy Israeli bombardment continued throughout the day Saturday, and in an attack that brought scathing criticism from the United Nations, Israeli tank fire killed two young brothers taking shelter at a United Nations school in the northern Gaza town of Beit Lahiya.

United Nations aid officials raised questions about whether the attack, and others like it, should be investigated as war crimes. The Israeli Army said that it was investigating the reports at the highest level, but that initial inquiries indicated that troops were returning fire from near or within the school.

On the cease-fire, Mr. Olmert said Israel was responding positively to peace efforts by President Hosni Mubarak of Egypt, in a clearly orchestrated move by two countries that see the Hamas movement in Gaza as a threat.

Israel will also wait to see the details of an Egyptian effort, supported by the United States, France, Britain and Germany, to stop the smuggling of arms, explosives, cash and men into Gaza through tunnels from Egypt.

Mr. Mubarak and President Nicolas Sarkozy of France will host a summit meeting on Sunday in the Egyptian resort of Sharm el Sheik to discuss the interdiction of smuggling and the reconstruction of Gaza after the Israeli air and land attack, which has left large areas of the crowded territory in ruins and without basic services like potable water and electricity.

Secretary of State Condoleezza Rice hailed Israel’s cease-fire announcement and said in a statement that the United States “expects that all parties will cease attacks and hostile actions immediately.”

That appeared unlikely as the truce’s 2 a.m. start neared early Sunday. In Gaza City, a Hamas spokesman in hiding, Fawzi Barhoum, said in a statement that “we will not accept the presence of a single soldier in Gaza,” according to Agence-France Presse. “The Zionist enemy must stop all its aggression, completely withdraw from the Gaza Strip, lift the blockade and open the crossings.”

Beyond the potential for an effective end to heavy fighting on Sunday, the shape of any lasting peace was far from clear.

The length of Israel’s occupation of Gaza has now been put in the hands of Hamas. The Israeli government says it will not sign any deal with the group, which is committed to Israel’s destruction and whose rule over Gaza the Israelis do not want to recognize. But Hamas is seen as likely to reassert political control over Gaza.

And Israel and Egypt will be under considerable pressure to reopen its crossings into Gaza for goods, given the size of the reconstruction required, and the crossings for people.

Particularly concerned about limiting smuggling into Gaza, the United States and Israel signed a “memorandum of understanding” on Friday in Washington that calls for expanded cooperation to prevent Hamas from rearming through Egypt. The agreement, which is vague, promises increased American technical assistance and international monitors, presumably to be based in Egypt, to crack down on the smuggling.

As important, the United States agreed to work with NATO partners to interdict arms smuggling into Gaza by land and sea from Syria and Iran, and in a letter, Britain, France and Germany also offered to help.

The summit meeting in Egypt on Sunday will also include Italy; Spain; Turkey; Ban Ki-moon, the United Nations secretary general; and a representative of the Palestinian Authority, which governs the Palestinian West Bank. The United States was to be represented by Margaret Scobey, the ambassador to Syria.

Although Mr. Sarkozy began the diplomatic process toward a cease-fire with Mr. Mubarak in the waning days of the Bush administration, it has been a deal shaped by Egypt and Israel.

Mr. Mubarak’s foreign minister, Ahmed Aboul Gheit, said that his country would not be bound by the memorandum of understanding agreed to by the United States and Israel and would not accept foreign troops on its soil. But officials of both Israel and the United States say Egypt has been showing a new seriousness about stopping the smuggling.

The Arab and Muslim world again appeared to be split into two camps. Egypt and Saudi Arabia have been openly critical of Hamas, pressing it to agree to a cease-fire. Qatar, meanwhile, which has close ties to both the United States and Iran, held a meeting with Syria, Iran, Mauritania and Hamas’s exiled political leader, Khaled Meshal, as the Palestinian representative. Mr. Abbas, who is supported by the United States and Egypt, had refused to go to Qatar. In Beit Lahiya, about 1,600 displaced Gazans have taken shelter at a school run by the United Nations Relief and Works Agency, or Unrwa, which cares for Palestinian refugees from the 1948-49 war and their descendants.

John Ging, the Gaza director of the agency, said that two brothers, ages 5 and 7, were killed about 7 a.m. by Israeli fire at the school. Their mother, who was among 14 others wounded, had her legs blown off.

“These two little boys are as innocent, indisputably, as they are dead,” Mr. Ging said. “The question now being asked is: is this and the killing of all other innocent civilians in Gaza a war crime?”

Christopher Gunness, the refugee agency’s spokesman, said: “Where you have a direct hit on an Unrwa school where about 1,600 people had taken refuge, where the Israeli Army knows the coordinates and knows who’s there, where this comes as the latest in a catalogue of direct and indirect attacks on Unrwa facilities, there have to be investigations to establish whether war crimes have been committed.”

The strike was the fourth time Israel has hit an Unrwa school during the war on Hamas. On Jan. 6, Mr. Ging said, 43 people died when an Israeli shell hit the compound of a school in Jabaliya. Israel has disputed the death toll and said it had been returning mortar fire from within the school compound.

Four Israeli soldiers, two of them officers, were seriously hurt by mortar fire in fighting on Saturday morning, the army said, suggesting that they were victims of friendly fire. Five others were also wounded by an antitank missile. The army said that Hamas had fired 15 rockets at Israel on Saturday, lightly wounding five Israelis, in a sharp reduction from daily attacks since the start of the war.

While the details are debated and the dead are counted, a critical long-term issue is whether the Gaza operation restores Israel’s deterrent. Israel wants Hamas, Hezbollah, Iran and the Arab world to view it as a nation too strong and powerful to seriously threaten or attack. That motivation is one reason, Israeli officials say, for going into Gaza so hard, using such firepower, and fighting Hamas as an enemy army.

The answer will not be known for many months, but the key to the Muslim world’s reaction is actually that of the Israeli public, said Yossi Klein Halevi, of the Adelson Institute for Strategic Studies in Jerusalem. “The Arabs take their cue from Israeli responses,” he said. “Deterrence is about how Israelis feel, whether they feel they’ve won or lost.”

Mr. Halevi cited the 1973 war — which Egyptians celebrate and Israelis mourn, though it ended with a spectacular Israel counterattack — and the 2006 war against Hezbollah in Lebanon.

Hezbollah’s leader, Hassan Nasrallah, apologized for the 2006 war on television, “but he quickly reversed himself to declare a wonderful victory when he saw the Israeli public declaring defeat,” Mr. Halevi said.

Even more important, perhaps, this Gazan war is a test case for any potential Israeli withdrawal from the occupied West Bank. If Israelis feel that the West Bank will turn into another kind of chaotic, Hamas-run Gaza, they will be unwilling to withdraw — especially if they believe that once they withdrew, and if they were attacked from the West Bank, they would not be allowed to respond with force.

“Gaza is an important test of whether we can defend ourselves within the 1967 boundaries,” Mr. Halevi said, noting that Hamas had been attacking Israel proper, not settlements. “Will we be able to defend ourselves if we need to from the West Bank? Will the international community let us?”

The Israeli public has stayed united behind the war as a necessary battle, despite serious misgivings about the death toll of Palestinian civilians and international condemnation. Even Meretz, a party of the Israeli left, supported the air war.

Hamas has modeled itself on Hezbollah, calling on Iranian support. Mr. Nasrallah once spoke of Israeli power as a spider web — impressive from afar, but easily brushed aside. This war against Hamas, Mr. Halevi said, “is the revenge of the spider.”

Workers fought a fire at a United Nations building in Gaza City, which was among those hit during Israeli shelling on Thursday.

Among the buildings hit in the center of Gaza City, the witnesses said, was one housing the headquarters of the United Nations Relief and Works Agency that assists Palestinian refugees and another occupied by several media organizations.

The United Nations secretary general, Ban Ki-Moon, visiting Jerusalem, said he expressed “strong protest and outrage” to Israel over the shelling of the United Nations compound, according to news reports.

Mr. Ban said Defense Minister Ehud Barak had told him the shelling was a “grave mistake,” the news reports said.

The Israeli military would not give precise details of its ground operations, but a spokesman said that “fierce fighting” was under way “relatively deep inside Gaza.”

The military push may be aimed at stepping up pressure on Hamas as cease-fire talks in Egypt entered a pivotal stage.

Overnight, Israeli planes struck around 70 targets, including a mosque in the southern town of Rafah used to stockpile rockets, and several squads of gunmen, the military said. Within two hours on Thursday morning, militants in Gaza launched 15 rockets and mortars against Israel, the military said, a marked increase in fire compared to Wednesday when there were 16 launches the entire day.

Palestinians arriving with injured relatives at Shifa Hospital in Gaza City on Thursday, some barefoot and in nightgowns, told of intense Israeli shelling in several neighborhoods including the Sabra and Tufah districts. Two television cameramen arrived for treatment after the building housing the media offices was hit. They had been filming from a window, they said.

As the Gaza death toll passed an estimated 1,000 people and concerns about the humanitarian situation inside Gaza grew, Egypt announced on Wednesday that it was making progress toward an interim cease-fire, with some officials predicting that one could be five to six days away. A senior Israeli defense official, Amos Gilad, arrived in Cairo on Thursday to continue the talks.

Also on Wednesday, nine Israeli human rights groups called for an investigation into whether Israeli officials had committed war crimes in Gaza. The groups say that tens of thousands of civilians in Gaza have nowhere to flee, the Gaza health system has collapsed, many people are without electricity and running water, and some are beyond the reach of rescue teams.

“This kind of fighting constitutes a blatant violation of the laws of warfare and raises the suspicion, which we ask be investigated, of the commission of war crimes,” the groups said in a news conference on the 19th day of the war.

The president of the International Committee of the Red Cross, Jakob Kellenberger, who spent Tuesday in Gaza City, agreed that the situation with civilians was dire but said that the principal hospital was making do with medical supplies, and that doctors, working around the clock, were mostly coping with the flow of the wounded.

“In general, they did not complain about the lack of equipment or material,” he said at a news conference in Jerusalem.

Hamas’s leaders met with Egyptian officials in Cairo and agreed in principle to a monitoring force in Gaza composed of Europeans to prevent weapons smuggling, said a senior Egyptian official. Israel’s defense minister, Ehud Barak, and his generals favor a temporary cease-fire of several days to a week, partly so that when President-elect Barack Obama is inaugurated next week it would be during a lull rather than in the middle of a battle, and his administration could offer its views on the next step, Israeli officials said.

The short-term cease-fire would, if successful, be followed by a negotiated yearlong truce, something that Egypt says Hamas favors if it includes an opening of commercial traffic into Gaza. But splits in Hamas exist between its leaders based in Syria and those in Gaza. The Gazans are more open to a weeklong break, while the leaders in Syria want something from Israel in return for holding fire.

Secretary General Ban Ki-moon of the United Nations arrived in Cairo Wednesday as part of a regional tour to press all parties to carry out a Security Council resolution calling for a cease-fire. He met with President Hosni Mubarak and then issued a plea for peace.

President Bashar al-Assad of Syria also called for a cease-fire, saying in an interview with the BBC that the effects of war could be more dangerous than war itself, “sowing seeds of extremism and terror around the region.”

Osama bin Laden, the leader of Al Qaeda, in a taped audio message, called on Muslims everywhere to fight Israel in a holy war.

The Israeli human rights groups that called for an investigation said that while they believed that it was legitimate for Israel to bomb military installations, it was a violation of international law to hit civilian sites and government buildings that contained no weapons.

The groups included the Israel section of Amnesty International, B’Tselem, Gisha and Physicians for Human Rights-Israel. Israeli Jews are firmly behind the government’s conduct of the war, with the human rights groups representing a small minority.

Mr. Kellenberger of the Red Cross said that Israel had facilitated his trip to Gaza and added that he had seen no evidence of the use of white phosphorus, an obscurant used in military conflicts that can be dangerous for civilians under certain circumstances. Palestinians say Israel is using it in Gaza.

Last week, the Red Cross issued an unusually harsh condemnation of Israel for refusing to allow its personnel into Gaza to rescue people trapped in battle. On Wednesday, Mr. Kellenberger said that although the situation remained critical, rescue missions had not been entirely shut down. The organization rescued 100 people trapped in Jabaliya, north of Gaza City, on Tuesday.

Israeli soldiers chanted slogans before entering Gaza on Sunday. Prime Minister Ehud Olmert said Israel was closer to its goals.

But news reports on Monday said Hamas militants fired as many as 10 missiles out of Gaza into southern Israel without causing casualties.

Overnight, the Israeli military said, its warplanes carried out fewer strikes than on some previous nights.

By midday Monday, the Israeli military said its warplanes had struck 25 targets including a mosque said to be used to store Hamas rockets and mortars. Facing accusations that its offensive has created a humanitarian crisis in Gaza, the military said 165 truckloads of aid were being allowed into Gaza.In Jerusalem on Sunday, Israel’s prime minister, Ehud Olmert, told the nation that Israel was “getting close to achieving the goals it set for itself,” but that “more patience, determination and effort are still demanded.”

Mr. Olmert was speaking in the public part of the regular Sunday cabinet meeting, and his words were broadcast to an Israeli populace that supports the war against Hamas in Gaza but is nervous about how and when it will end.

Mr. Olmert gave no time frame, but said Israel “must not miss out, at the last moment, on what has been achieved through an unprecedented national effort.”

The Israeli military said on Monday that warplanes attacked five Hamas operatives along with weapons caches, tunnels and other targets, while Israeli gunboats fired from the sea. Israeli officials also said Sunday that the military had been sending reserve units into Gaza since Thursday. They did not specify the number of reservists. The announcement appeared aimed at adding pressure on Hamas but it also raised the possibility of an expansion in the conflict, which began Dec. 27. It was not clear Monday whether the so-called “third phase” of the war had been approved by Israeli leaders.

On Monday Egypt planned to convene negotiations aimed at a cease-fire in Gaza, where the Israeli military assault to silence rocket fire and tunneling by Hamas and other militants opposed to Israel’s existence has wrought extensive death and destruction.

Nearly 900 people have been killed, according to Palestinian Health Ministry officials. Thirteen Israelis have been killed, Israel has said.

European diplomats involved in the Egypt negotiations said Sunday that the next 48 hours would be crucial for Israel to decide if a durable cease-fire can be achieved.

The Israeli cabinet secretary, Oved Yehezkel, told reporters that in the cabinet meeting the heads of army intelligence, Maj. Gen. Amos Yadlin, and of the Shin Bet security service, Yuval Diskin, said, “It is the inclination within Hamas to agree to a cease-fire, given the harsh blow it received and given the absence of accomplishment on the ground.”

The Israelis said this view inside Gaza was a contrast to the “unyielding stands” of the exiled Hamas leadership in Damascus, Syria, in particular Khaled Meshal, the political director. But Hamas “is not expected to wave a white flag” and is reserving rockets and weaponry to fire at the end of the conflict, the intelligence chiefs said.

Another senior Israeli security official said that Israeli soldiers had “confirmed through their sights” the killing of 300 Hamas and Islamic Jihad fighters on the ground in Gaza, and that Hamas units were making mistakes and fighting without clear direction.

“I can say with a high level of confidence that for two days, what we have been hearing repeatedly is that Hamas inside Gaza is eager — eager — to achieve a cease-fire,” said the senior official, who spoke on condition of anonymity because of the issue’s delicate nature. “This is as opposed to the leadership in Damascus that is willing to fight to the last Palestinian.”

The Israelis were clearly all pushing a concerted message, but no official provided details on how Israel supported its assertion. It was impossible to get a response from Hamas leaders in Gaza, because they were in hiding from Israeli military strikes.

On Saturday, the Hamas political director in exile, Mr. Meshal, said in Damascus that Hamas would not consider a cease-fire until Israel ended the assault and opened all crossings into Gaza. He said that the ferocity of the Israeli campaign had crossed the line and called it a “holocaust,” adding, “You have destroyed the last chance for negotiations.”

Israel and the United States are trying to secure agreement on a deal brokered by Egypt that would mean a Hamas commitment to stop all rocket firing into Israel and an Egyptian commitment to block smuggling tunnels into Gaza, to stop the resupplying of Hamas with weaponry and cash. In return, Israel would agree to a cease-fire and the opening of its crossings into Gaza for goods and fuel and the opening of the Rafah crossing into Egypt, with European Union supervision.

Tony Blair, the former British prime minister and now an international envoy to the Palestinians, said in an interview that “the only way this is going to stop is if there is a genuine plan to end the smuggling into Gaza and a genuine plan to open the crossings.”

Mr. Blair will be in Cairo on Monday, as will a senior Israeli Defense Ministry official, Amos Gilad. A Hamas delegation is already in Cairo talking to the Egyptians through the intelligence chief, Omar Suleiman. If the Egyptian effort fails, Israeli officials said, the military is likely to go to a “third stage” of the war against Hamas in Gaza, with the reserve troops thrown into the battle.

An expansion of the war would most likely mean Israeli troops moving into southern Gaza, to take a strip of land at least 500 yards wide inside Gaza at the Egyptian border. Israel has been bombing the area to try to destroy smuggling tunnels between Gaza and Egypt.

Mr. Olmert and his two top cabinet ministers, Defense Minister Ehud Barak and Foreign Minister Tzipi Livni, were reported to disagree about the best way to win the war and consolidate Israeli gains. But they are under pressure from the army to decide on whether to expand the war or end it, in part because the soldiers become easier targets unless they are constantly moving.

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There was a new development on Sunday in the investigation into one of the deadliest attacks so far — an Israeli mortar strike near a United Nations school on Tuesday that killed up to 43 Palestinians. The newspaper Haaretz reported that a military investigation had concluded that two Israeli shells hit a Hamas mortar unit that had fired first, but that an errant Israeli shell hit near the school.

The army later rebutted the article, saying its initial inquiry showed “mortars were fired from within the school” at Israeli forces nearby, “and those forces returned fire.”

United Nations officials have denied that any Palestinian fighters were in the school grounds and called for an independent international investigation, and the army had earlier gone back and forth about whether the Hamas mortars were fired within the school or near it.

Palestinians set down the bodies of two members of the Samouni family during a funeral in Gaza City on Monday.

Israeli troops swarmed Zeitoun shortly after the ground invasion of Gaza began a week ago, and members of the extended Samouni family said they were moved from house to house as soldiers took over the neighborhood. On Monday, with nearly 100 Samounis huddled together in one house, the shooting and the shelling began, according to accounts of family members and witnesses that were partly corroborated by the Red Cross and the United Nations.

Thirty Samounis died, not all of them quickly. Ahmed al-Samouni, 16, survived.

“I could feel the blood dripping inside my head,” Ahmed said, recalling the days he lay wounded in the bombed-out building. “My father was crawling — he couldn’t move his legs,” he said.

His cousin Abdallah, 10, was trying to stand up but kept falling down; his brother Yaqoub, 12, kept removing large pieces of shrapnel from his own stomach; and his sister Amal, 9, was not moving at all. Another brother, Ishaq, 12, was wounded in the legs. He bled for two days before he died.

Ahmed, speaking from his hospital bed, said he wanted to call for help. But his mother, Laila, was among the dead, and her cellphone was nowhere to be found.

The story of the Samouni family has horrified many since Red Cross officials on Wednesday publicized their discovery of four emaciated Samouni children trapped for days in a home with the corpses of their mothers. The Red Cross said the Israeli military denied its paramedics access to the area for several days after the ground invasion began on Jan. 3, part of the offensive against Hamas that Israel says is intended to stop the firing of rockets into southern Israel.

Israeli officials said they were still looking into the Zeitoun episode. A military spokeswoman, Maj. Avital Leibovich, said Monday that the army had “no intention of harming civilians.” Hamas, which governs Gaza, “cynically uses” civilians for cover by operating in their midst, she said.

But some international aid officials are arguing that the plight of civilians in Zeitoun, as well as the shelling of a United Nations school where civilians had sought refuge, should be investigated as war crimes.

“Accountability must be ensured for violations of international law,” Navi Pillay, the United Nations high commissioner for human rights, said in an address in Geneva to a special session of the Human Rights Council focused on Gaza. The council has a reputation for censuring Israel. Ms. Pillay is a respected South African judge who recently assumed the top United Nations human rights job, which is separate from the council.

Ms. Pillay said, “Violations of international humanitarian law may constitute war crime, for which individual criminal responsibility may be invoked.” She suggested that the council weigh dispatching a mission to assess violations committed by both sides.

The Israeli military has not said whether the strike on the house in Zeitoun was intentional or a mistake. In the case of the United Nations school, Israel has said that Hamas militants were firing mortars from a location near the school.

According to Ahmed and other witnesses interviewed at the hospital, soldiers came to several of the Samouni homes that make up a section of Zeitoun soon after the ground invasion started. They told family members to vacate their homes and to gather together in one home down the street. Ahmed said they were moved a second time as well, until nearly 100 of his relatives crowded into one house.

Soldiers searched and occupied the now-empty houses. The Zeitoun neighborhood is strategically located and is known to have many supporters of Hamas. Ahmed said the Israelis wanted to turn it into “a military camp.”

Samouni family members did not deny that Hamas militants operated in the area. A family member said there was no active Hamas resistance in the immediate vicinity, although militants were firing rockets at Israel a little more than a mile away.

At about 6 a.m. on Monday morning, Ahmed said, tanks started demolishing a wall of the house where the extended clan was sheltered. His father moved toward the door, presumably to warn the soldiers that civilians were inside, but the troops started shooting, he said.

The shooting then stopped, and the soldiers appeared to withdraw. But a short time later, three rockets and several shells hit the building and tore apart the rooms where his family was gathered.

Ahmed said he and his brother Yaqoub pulled blankets over their relatives and managed to shut the doors in an attempt to hide from the tanks and soldiers outside. Everyone was crying, he recalled, and he did not immediately realize the scope of the damage. Some relatives, like Masouda Samouni, 20, Ahmed’s sister-in-law, managed to crawl out by themselves and arrived at the hospital that same day. A few hours after the attack on Monday, she recounted how she had lost her mother-in-law, her husband and her 10-month-old son.

At that time, witnesses and hospital officials believed that 11 members of the extended family were killed and 26 wounded, with five children age 4 and under among the dead. The first survivors who arrived at the hospital may not have been aware of the full extent of the disaster and apparently had not counted all those left behind.

Ahmed, rescued nearly three days later, named 27 relatives who died in the building where he was hiding; the Red Cross said three more corpses were found in a house nearby.

The survivors ate tomatoes, drank water and cooked noodles over a fire, but tried to avoid attracting the attention of soldiers in the area. Relatives who escaped repeatedly asked the Red Cross to send help, but Red Cross officials said their requests to respond to the emergency were rejected by the Israelis during the initial days of the siege.

It was 3:30 p.m. on Wednesday when help finally came, half an hour before the end of a three-hour pause in the fighting ordered that day by Israel to allow humanitarian aid and rescue workers to enter Gaza.

Antoine Grand, the head of Red Cross operations in the Gaza Strip, said in a telephone interview on Thursday that the first rescue team on Wednesday had to leave the dead and take out only the wounded, “horrible as that seems,” because they had only limited time and only four ambulances.

“We had no other choice,” Mr. Grand said.

He added that the ambulances had to stop on one side of an earth mound put up by the military. The team had to walk a mile to the houses and bring back the wounded in a donkey cart.

On Thursday, they went back to the same area and brought out another 103 survivors, three of them wounded.

A report issued by the United Nations Office for Humanitarian Affairs on Thursday, based on telephone interviews with several members of the Samouni family, largely corroborated Ahmed’s version of events, saying about 30 people were killed when the house was shelled repeatedly. The report said the attack on the Samouni home was one of the “gravest incidents” in the Israeli campaign.

In another statement issued on Friday, the humanitarian affairs office emphasized that its report was not intended to render a legal verdict on the attack.

In a rare public statement on Thursday, the Geneva-based International Committee of the Red Cross said it believed that in this instance, the Israeli military failed to meet its obligation under international humanitarian law to care for and evacuate the wounded. The delay in permitting entry to rescue services was “unacceptable,” it said.

The rescue team found “four small children next to their dead mothers in one of the houses,” the Red Cross said. “They were too weak to stand up on their own.”

The Red Cross added that Israeli soldiers were posted at a military position some 80 yards away from the house, and there were several other army positions and two Israeli tanks nearby.

Mark Regev, a spokesman for the Israeli government, said Friday that it was important that “we have better channels of communication and coordination” with the Red Cross and other aid groups. He said Israel had an interest in the Red Cross’s “successfully carrying out its mission.”

Palestinians gathered to receive flour at a United Nations food distribution center in Gaza City on Thursday.

In a statement after a cabinet meeting, Prime Minister Ehud Olmert said the Israeli military would “continue acting to protect Israeli citizens and will carry out the missions it was given,” according to news reports.

Officials from Hamas dismissed the U.N. resolution, according to news reports, although one official said it was being studied.

In Beirut, a Hamas spokesman, Raafat Morra, said the resolution “does not suit us because it is not in the best interest of the Palestinian people,” Agence France-Presse reported.

As the war continued unchecked on Friday, the Israeli military said its forces attacked more than 50 targets in overnight despite the U.N. vote on Thursday night calling for “an immediate, durable and fully respected cease-fire.”

Israeli warplanes attacked launching sites and missile-manufacturing facilities, the military said, while witnesses reported seeing rockets fired out of Gaza into southern Israel. The casualty toll was not immediately known. One Israeli air strike destroyed a five-story building, killing at least seven people, Hamas security officials told The Associated Press.

The developments came as international aid groups lashed out at Israel, saying that access to civilians in need is poor, relief workers are being hurt and killed, and Israel is woefully neglecting its obligations to Palestinians who are trapped, some among rotting corpses in a nightmarish landscape of deprivation.

The latest accusation concerning the treatment of civilians came on Friday when the United Nations Office for the Coordinator of Humanitarian Affairs said Israeli shelling killed 30 people who had been ordered along with 80 others to evacuate their homes and gather in a single apartment house.

“The next day the house was shelled,” Allegra Pacheco, a spokeswoman for the United Nations office, told the BBC, quoting unidentified witnesses.

The U.N. agency said the house was located in the Zeitoun district of Gaza City, the same area where the International Committee of the Red Cross reported Thursday that its representatives found four small children cowering next to their mothers’ corpses on Wednesday.

In a rare and sharply critical statement, the Red Cross said it believed that “the Israeli military failed to meet its obligation under international humanitarian law to care for and evacuate the wounded.”

Israeli officials said that they were examining all the allegations, that they did not aim at civilians and that they were not certain that the source of fire that killed and wounded the United Nations drivers was Israeli.

“We do our utmost to avoid hitting civilians, and many times we don’t fire because we see civilians nearby,” said Maj. Avital Leibovich, chief army spokeswoman for the foreign media. “We are holding meetings with U.N. officials to try to work out a mechanism so that their work can go forward.”

She said that the army learned of the Red Cross allegations in a media report, and that the committee had not yet presented the evidence of what she called “these very serious allegations” to the army.

Earlier this week, members of an extended family, the Samounis, said they had been ordered to evacuate their homes in Zeitoun and gather in a single dwelling. It was not immediately clear if the complaints by the U.N. agency on Friday related to the same family.

Initial reports about the incident on Monday said 11 members of the Samouni extended family were killed and 26 wounded, according to witnesses and hospital officials, with five children age 4 and under among the dead. But the death toll rose as more bodies were found. The Red Cross said on Thursday that Israel had denied its representatives access to the area for several days.

Separately, the United Nations declared a suspension of its aid operations after one of its drivers was killed and two others were wounded despite driving United Nations-flagged vehicles and coordinating their movements with the Israeli military. The United Nations secretary general, Ban Ki-moon, called for an investigation by Israel for a second time in a week of the more than 40 deaths near a United Nations school from Israeli tank fire on Tuesday.

The Red Cross also said it was restricting its operations on Friday after one of its trucks was hit by small arms fire.

At the United Nations , fourteen nations approved the Security Council resolution urging a cease-fire, with the United States abstaining. Secretary of State Condoleezza Rice said the United States abstained , which left it unclear how a cease-fire would be enforced, because it wanted to see whether mediation efforts undertaken by President Hosni Mubarak of Egypt would succeed. The United States did not veto the resolution because Washington supports its overall goals, she said.

The resolution called for a cease-fire that would lead to the “full withdrawal” of Israeli forces from Gaza, the passage of humanitarian aid to the Palestinians and an end to the trafficking of arms and ammunition into the territory.

Reporting was contributed by Neil MacFarquhar from the United Nations; Rachel Donadio from Rome; Isabel Kershner and Steven Erlanger from Jerusalem; Taghreed El-Khodary from Gaza; and Alan Cowell and Caroline Brothers from Paris.

Soldiers rested on the Israeli side of the border with Gaza during the three-hour cease-fire on Wednesday.

The rockets, presumably launched in support of Hamas, could presage the opening of a second front. The Israeli Army, in a brief statement, said it “responded with fire against the source of the rockets,” which landed near the town of Nahariya. Two Israelis were slightly wounded, the police said.

So far there has been no claim of responsibility. A spokeswoman for the militant group Hezbollah, which triggered a war with Israel in 2006 by firing rockets into northern Israel from Lebanon, said an investigation was underway. “We are still looking for information about it,” she said.

Prime Minister Fuad Siniora immediately condemned the attack.

In 2006, after the kidnapping of an Israeli soldier just outside Gaza, a large Israeli operation there was overshadowed by Israeli’s massive response to an attack in the north by Hezbollah, which turned into what is known as the Second Lebanon War.

On Wednesday, Israel had said that it would send senior officials to talk with Egypt about halting the conflict in Gaza, but there were no immediate signs of a diplomatic breakthrough, and fighting between Israel and Hamas militants continued after a three-hour lull for humanitarian aid to be distributed.

International pressure for a negotiated cease-fire intensified after Israeli shells killed some 40 people at a United Nations school in Gaza on Tuesday. Israel said Hamas militants had fired mortar shells from the school compound prior to Israel’s shelling.

Israel suspended its military operations in Gaza for three hours on Wednesday to allow humanitarian aid and fuel for power generation to reach Gazans, who used the afternoon break to shop.

But fighting resumed soon afterward and continued into a 13th day on Thursday. For the second successive day, Israel said Thursday it would pause its offensive for three hours to permit Gaza’s population to seek medical and food supplies, The Associated Press reported.

On Wednesday evening, the Israeli Army dropped leaflets warning the citizens of Rafah, next to the border with Egypt, to leave their homes. Israel has been bombing the tunnel networks through which arms and consumer goods are smuggled from Egypt into Gaza.

The rockets from Lebanon fell in residential areas. Shimon Koren, head of the northern district police, instructed residents of Nahariya and Kabri to enter bomb shelters and he instructed residents in nearby localities to open their shelters. School was cancelled in Nahariya and nearby Shlomi. The Israeli government said it welcomed the efforts of France and Egypt to work out a durable cease-fire. It said it would end its assault if Hamas stopped firing rockets into Israel and ended the smuggling of weapons from Egypt. It said that if a durable cease-fire took hold, it would reopen border crossings into Gaza for goods and people. But Israeli and Hamas officials both denied an assertion by the French president, Nicolas Sarkozy, that a cease-fire had been agreed upon.

“There is an agreement on general principles, that Hamas should stop rocket fire and mustn’t rearm,” a senior Israeli official said Wednesday evening. “But that’s like agreeing that motherhood is a good thing. We have to transform those agreed principles into working procedures on the ground, and that’s barely begun.”

The government spokesman, Mark Regev, said that “the challenge now is to get the details to match the principles.”

There were early signs that a formal diplomatic negotiation could begin after days of fighting. Egypt’s chief of intelligence, Omar Suleiman, is expected to serve as a go-between for Israel and Hamas. Two Israeli officials — a senior aide to Prime Minister Ehud Olmert, Shalom Turgeman, and a senior defense official, Amos Gilad — are expected to go to Egypt on Thursday to begin discussions, Israeli officials said.

The United States has been involved behind the scenes, senior Israeli and French officials said, with Secretary of State Condoleezza Rice “constantly on the phone” with Mr. Olmert, according to one Israeli official.

In Washington, the White House spokeswoman, Dana M. Perino, said of talks about a cease-fire: “As I understand, the Israelis are open to the concept, but they want to learn more about the details; so do we.”

At the United Nations, several Arab delegates said Wednesday night that they thought they now had enough votes to approve a Security Council resolution calling for an immediate cease-fire. That would likely put the United States and other Western powers, which oppose a binding resolution, in the awkward position of having to veto a cease-fire.

A senior French official in Paris said that Mr. Sarkozy’s earlier comment about an agreement on a cease-fire was misunderstood: “The plan is not a cease-fire; the plan is a road map toward a cease-fire.” One crucial aspect of any deal is how to prevent new smuggling tunnels from being built under Egypt’s border with Gaza.

The senior Israeli official raised the possibility of reaching “tacit agreements” with Hamas to end rocket fire, while also persuading Egypt to allow American and perhaps European army engineers to help seal its border with Gaza above and below ground.

Hamas is insisting that any new arrangement include the reopening of border crossings for trade with Israel and the reopening of the Rafah crossing into Egypt for people.

President Hosni Mubarak of Egypt has said that a 2005 agreement on the Rafah crossing, reached with Israel and the Palestinian president, Mahmoud Abbas of Fatah, must be respected. That agreement called for a Palestinian Authority presence at the crossing, supervision by European Union monitors and Israeli video surveillance of who entered and left.

Hamas wants to control the crossing itself and is not eager to cooperate with Fatah, its -rival.

In Washington, President-elect Barack Obama said Wednesday that upon taking office he would “engage immediately” in the Middle East crisis and that he was “deeply concerned” about the loss of life on both sides. “I am doing everything that we have to do to make sure that the day I take office we are prepared to engage immediately in trying to deal with the situation there,” he said at a news conference. “Not only the short-term situation but building a process whereby we can achieve a more lasting peace in the region.”

In Gaza, John Ging, the director of Gazan operations for the United Nations Relief and Works Agency, visited the school in the Jabaliya refugee camp where Israeli shells fell Tuesday. He denied that Hamas militants had fired mortar shells from within the school compound and called for an international investigation into the attack, which he said had killed 40 people.

Israeli officials said they were continuing to investigate, but reiterated that Hamas had been using the school as a base. Mr. Gilad, the defense official, told Israeli Army radio: “This school served as a base for Hamas men whose identity we know. They fired from inside the school compound, and the army fired back at the source. The time was after school hours, and this school is an example of the cynical and cruel use Hamas does with civilian facilities.”

Casualty figures are hard to verify, but officials at Shifa Hospital in Gaza City and the Gazan Ministry of Health said 683 Palestinians had died since the conflict began Dec. 27, including 218 children and 90 women. They said 3,085 had been wounded. The Palestinian Center for Human Rights in Gaza said 130 children age 16 or under had died. The United Nations estimated a few days ago that a quarter of the dead were civilians.

But Palestinian residents and Israeli officials say that Hamas is tending its own wounded in separate medical centers, not in public hospitals, and that it is difficult to know the number of dead Hamas fighters, many of whom were not wearing uniforms.

Israel says it has killed at least 130 Hamas fighters. Ten Israelis have been killed during the offensive, including three civilians. Most of the seven dead Israeli soldiers were killed in so-called friendly fire.

A wounded Palestinian being carried on Tuesday near the United Nations school in Jabaliya, Gaza, that Israeli forces shelled.

The announcement by officials in Jerusalem came a day after Israeli mortar shells killed as many as 40 Palestinians, among them women and children, outside a United Nations school in Gaza.

Mark Regev, the spokesman for Prime Minister Ehud Olmert, said the idea behind relief corridors was to permit a flow of food and other aid to a population said by U.N. officials to be facing a humanitarian crisis. A statement late Tuesday from Mr. Olmert’s office said the pause would “entail opening geographic areas for certain periods of time during which the population would be able to equip itself and receive the assistance.”

The Associated Press quoted the Israeli B’Tselem human rights group as saying the military had informed it of a planned lull in the afternoon between 1 p.m. and 4 p.m. local time. Military offcials said the Israeli measures would allow Gaza residents to leave their homes to seek medical help and buy food.

International relief agencies have warned that the humanitarian situation in Gaza was increasingly dire. Three-quarters of the 1.5 million residents are currently without power, and hundreds of thousands are without running water, international agencies have said.

John Ging, the chief of operations for the United Nations Relief and Works Agency, said the pause was “not a solution but it’s a first step.”

With the death toll mounting, President Shimon Peres told Sky News in an interview on Wednesday that Israel would also study cease-fire proposals put forward by Egypt. Agence France-Presse reported on Wednesday that Israeli tanks which reportedly pushed into the southern Gaza city of Khan Yunis pulled out before dawn as fighting continued elsewhere. Witnesses said explosions and artillery fire continued to be heard from Gaza as the planned three-hour pause approached.

In Gaza City, some still reeled from events on Tuesday when Israeli mortar fire struck near a U.N. school where many people were taking refuge. The Israeli military contended that Hamas fighters had fired mortars from the school compound, and U.N. officials called for an independent inquiry into the episode.

The rising civilian death toll in crowded Gaza heightened international urgency to end the combat. American and European diplomats said it was highly likely that Mr. Olmert would travel to Egypt on Wednesday to discuss a cease-fire.

But officials in Cairo said on Wednesday it was not definite that the Israeli leader would make the trip. Israel has said it will not end the operation in Gaza until it has crushed Hamas’s ability to fire rockets into its civilian areas.

That has not happened. The Israeli military reported on Wednesday that a rocket fired from Gaza landed in a yard in the southern Israeli city of Ashkelon and nine people were treated for shock. Three other rockets landed elsewhere.

On Tuesday, one rocket reached farther than ever into Israeli territory, only 20 miles from Tel Aviv, and wounded an infant.

With another day of gory news reports inflaming the Arab world, Israel contended that the deaths at the school, at the Jabaliya refugee camp north of Gaza City, demonstrated Hamas’s callousness toward the lives of Palestinian civilians.

The Israeli Defense Forces said that their troops had fired several mortar shells near the school in response to mortar fire from the school compound.

“They shot back to save their own lives,” said Ilan Tal, an Israeli military spokesman and a brigadier general in the reserves. Among the dead, the military said in a statement, were “Hamas terrorist operatives and a mortar battery cell.”

The military identified two Hamas operatives, Imad Abu Asker and Hassan Abu Asker, as having been killed.

A young witness from Jabaliya, Ibrahim Amen, 16, said that he had seen one of the militants, whom he identified as Abu Khaled Abu Asker, in the area of the school right before the attack.

Ibrahim said he saw the militant after he answered calls for volunteers to pile sand around the camp “to help protect the resistance fighters.” Ibrahim went to pile sand near the school with his brother, Iyad, 20, who was then injured by the Israeli mortar fire.

The night before, the United Nations said, three Palestinian men were killed in an Israeli attack on another United Nations school for refugees in Gaza.

“These attacks by Israeli military forces which endanger U.N. facilities acting as places of refuge are totally unacceptable and must not be repeated,” the United Nations secretary general, Ban Ki-moon, said in a statement. “Equally unacceptable are any actions by militants which endanger the Palestinian civilian population.”  United Nations officials initially put the Jabaliya death toll at 30 and said 55 were wounded, with several in critical condition. Palestinian hospital officials said 40 people had been killed, among them 10 children and 5 women.

The death toll in Gaza reached around 640 on Tuesday, according to Palestinian health officials. The United Nations has estimated that about one-fourth of those killed were civilians, though there have been no reliable and current figures in recent days.

International efforts to halt the violence appeared to be moving into a higher gear.

At the United Nations, the Security Council held a high-level meeting attended by the Palestinian president, Mahmoud Abbas, and many foreign ministers to discuss the situation in Gaza. Mr. Abbas and other senior Arab officials supported a resolution calling for an immediate cease-fire, which was introduced by Libya.

But some members of the Security Council, including the United States, withheld support for any resolution because of efforts in the Middle East to achieve a cease-fire.

President Hosni Mubarak of Egypt said at a news conference in Sharm el Sheik, Egypt, with President Nicolas Sarkozy of France that the Israelis and the Palestinians should accept a cease-fire to give Cairo time to continue its efforts toward a durable long-term solution.

Israeli and American officials insist that a cease-fire would have to await guarantees that no more weapons would be smuggled into Gaza through tunnels from Egypt; a possible mechanism for that is the stationing of international observers along the border with Egypt.

President-elect Barack Obama broke his silence about the Gaza fighting on Tuesday, telling reporters, “The loss of civilian life in Gaza and Israel is a source of deep concern for me.”

Israeli losses have also risen since the ground invasion began on Saturday. The military said that three of its soldiers were killed late Monday night when an Israeli tank shell was mistakenly fired at a building they occupied.

A fourth soldier was also killed Monday night, very possibly also by an Israeli tank shell, the military said. Two soldiers, including one on Tuesday, have been killed in clashes with Hamas.

Before the Israeli ground campaign began, three Israeli civilians and a soldier were killed by rockets fired from Gaza at southern Israel.

In Al-Nasir, a district of Gaza City, families fleeing the fighting in the north poured into a United Nations boys’ school. Thirty members of the extended al-Sultan family from Beit Lahiya, including more than 20 children, huddled in one small classroom.

Ayisha al-Sultan, 36, who is married to a heart surgeon, said she had left behind a comfortable villa where each of her five children has a separate room.

“Now look at us,” she said. “At night we covered the floor tiles with paper for the kids to sleep on. We took off our jackets and covered them.”

Gaza residents took refuge in a United Nations school as Israel’s offensive continued with artillery, helicopter and tank fire.

Casualties were reported mounting on both sides as the military confrontation broadened. News reports said Israeli forces were probing deeper into southern Gaza after concentrating their initial thrust in the north of the coastal strip.

Defying Israeli and international demands, Hamas militants in Gaza fired more rockets into Israel Tuesday, one of them falling in the town of Gadera, less than 20 miles south of Tel Aviv, the Israeli Army said.

The target was the furthest north that any of the hundreds of missiles fired from Gaza has yet struck since the Israeli offensive began.

The location was significant to many Israelis since Gadera, about 25 miles north of Gaza, is perceived as being linked to Tel Aviv, meaning that central Israel may now be a vulnerable target for Hamas rockets along with the southern cities that have borne the brunt of the missile fire. Shrapnel from the attack slightly injured a three-month-old baby, the army said.

Since launching its ground offensive into Gaza on Saturday, Israel has killed 130 Hamas fighters, Israeli officials say. Hamas has killed five Israelis by rocket fire and in military encounters since the conflict began.

The Israeli army said on Tuesday that three Israeli soldiers were killed in tank-fire directed at a building they had occupied in northern Gaza, and a fourth soldier was killed in a separate incident, apparently also caused by a shell from a tank.

Since the operation began, Israeli officials in Washington said, the number of rocket and mortar attacks from Gaza has fallen to about 20 a day from a peak of 80 on Christmas Day. “The situation has obliged them to contract and pull back the rockets,” said Jeremy Issacharoff, the Israeli deputy chief of mission in Washington. “The rate of attrition is important,” he said, noting that Hamas was now launching fewer rockets than Israeli forces had expected.

In the latest phase of the fighting, Israel Radio quoted witnesses as saying Israeli forces were pushing toward Khan Yunis in southern Gaza, but details of the fighting there were sparse.

In the north of Gaza, three Palestinian men were killed late Monday night when a United Nations Relief and Works Agency school compound was hit by Israeli fire, according to a statement released on Tuesday by the organization, which provides assistance to registered Palestinian refugees. More than 400 Palestinians from northern Gaza were taking refuge in the school in Gaza City at the time, and the building was clearly marked as a United Nations installation, the statement said.

The latest fighting coincided with a new and inconclusive diplomatic effort to bring pressure on Hamas to halt the rocket attacks — one of Israel’s pre-conditions for a ceasefire, along with the destruction of Hamas as a fighting force and measures to prevent the Islamic militants from re-arming.

In Damascus President Nicolas Sarkozy of France met with President Bashar al-Assad of Syria after holding earlier talks in Egypt and discussions with Israeli leaders and Palestinian officials in the West Bank. Hamas is headquartered in Syria, and Mr. Assad is key ally of both Hamas and the Islamist Hezbollah movement in Lebanon. There was no immediate indication that the French leader had secured a commitment from Mr. Assad to put pressure on Hamas.

After talks with Mr. Sarkozy, Mr. Assad told a news conference that Israeli leaders “have not learned the lessons of the war in Lebanon” in 2006 when Hezbollah emerged politically strengthened from a bruising battle with Israel.

“Israel is falling into the same trap again and the Israelis will pay the highest price,” Mr. Assad said, calling the Israeli offensive a “war crime.”

Mr. Sarkozy said the violence “must stop immediately, as soon as possible.” He described the fighting in Gaza as “unbearable.”

Both sides in the Gaza conflict have adopted uncompromising positions.

On Monday, the Israeli foreign minister, Tzipi Livni, said after a meeting with officials from the Czech Republic, Sweden and France that Israel would “change the equation” in the region. She added that in other conflicts, “countries send in forces in order to battle terrorism, but we are not asking the world to take part in the battle and send their forces in — we are only asking them to allow us to carry it out until we reach a point in which we decide our goals have been reached for this point.” Israeli officials have said repeatedly that they are not ready to accept any cease-fire proposal that did not guarantee a permanent stop to rocket attacks as well as smuggling of weapons through tunnels under Gaza’s border with Egypt.

The Hamas leader Mahmoud Zahar, speaking from a hiding place in a recorded speech on Hamas television, said: “The Israeli enemy in its aggression has written its next chapter in the world, which will have no place for them. They shelled everyone in Gaza. They shelled children and hospitals and mosques, and in doing so, they gave us legitimacy to strike them in the same way.”

Palestinian medical officials estimated that the death toll during the war exceeded 560 on Tuesday. The United Nations estimated that about a quarter of those killed were civilians.

Israel said it had hit some civilian targets because they housed rockets, launchers or militants. It offered limited evidence of its claim.

Toward night on Monday, northern Gaza was the site of heavy fighting, including artillery, helicopter and tank fire, witnesses said. Plumes of smoke were visible in the night sky.

Inside Gaza City, windows are blown out, electricity is cut and drinking water scarce. While phones rang with the recorded threats against Hamas, leaflets dropped from airplanes littered the streets, saying: “Hamas is getting a taste of the power of the Israeli military after more than a week and we have other methods that are still harsher to deal with Hamas. They will prove very painful. For your safety, please evacuate your neighborhood.”

Israeli officials hope an eventual deal will be struck without engaging directly with Hamas, but Mark Regev, the spokesman for Prime Minister Ehud Olmert, said Israel would not exclude a tacit understanding with Hamas.

“The endgame for us is threefold: that Hamas’s military machine would be substantially destroyed; two, Hamas understands that shooting rockets means paying a price they don’t want to pay; and three, there are mechanisms in place to prevent Hamas from rearming,” Mr. Regev said.

But as the offensive unfolds, so, too, evidence is mounting of a severe humanitarian crisis.

Maxwell Gaylard, United Nations humanitarian affairs coordinator, said at a Jerusalem news briefing on Monday that because of the attacks, people could not reach available food.

Children are hungry, cold, without electricity and running water, he said, “and above all, they’re terrified. That by any measure is a humanitarian crisis.”

Smoke rose from central Gaza as Israeli soldiers crossed the border on Sunday.

Witnesses said the Israeli forces had punched across Gaza, bisecting its northern and southern parts, and had taken over certain strategic areas, including what the military has described as rocket launching sites.

The ground campaign came after a week of intense airstrikes. Israel’s stated goal was to destroy the infrastructure of Hamas, the Islamic group that controls Gaza’s government, and to significantly decrease the threat to southern Israel from Palestinian rocket fire.

In a telephone briefing for a group of foreign correspondents, a senior Israeli military official said that Israeli troops would hold the areas they have taken inside Gaza at least for the duration of the operation to prevent militants from returning to fire rockets from there.

“We don’t plan to retake the Gaza Strip but there are several places we control now and will control later,” he said. “If it will be needed, we are prepared to stay there.”

The military has warned that the campaign could take “many long days.”

Even with Israeli forces on the ground, though, Hamas continued its rocket fire. About 25 rockets were launched at southern Israel by Sunday afternoon, the military said. One hit a house in the Israeli border town of Sderot. Touring the town some time later, Michael R. Bloomberg, the mayor of New York, had to be rushed into a protected space when Sderot’s incoming rocket alert sounded.

Most of the fighting early Sunday was taking place in northern and eastern Gaza, in areas not far from the Israeli border. But at least five civilians were killed and many wounded on Sunday morning when Israeli shells or rockets landed in the market of Gaza City while people were stocking up on supplies.

The Israeli military said that they had “hit” dozens of armed Hamas operatives during exchanges of fire overnight. No reliable figures of casualties were immediately available from Palestinian officials.

The Israeli military also said that 30 soldiers had been wounded, two seriously, in clashes and from shrapnel.

The senior military official said that Hamas was using methods “imported from Iran and Hezbollah,” the Lebanese militant group. Those methods, he said, were “guerrilla concept and tactics, exploiting both open areas and those of highest density of population.” He said there had not been much man-to-man combat so far, and that Hamas was fighting back mostly with mortars and improvised explosive devices, or I.E.D.s.

Wounded civilians poured into the emergency room of Shifa Hospital in Gaza City on Sunday, including women and children. Two young cousins and a 5-year-old boy from another family were killed by shrapnel as they played on the flat roofs of their apartment buildings, after having been cooped up inside for long hours.

A woman who came to the hospital with a daughter, 15, who was wounded by shrapnel, said that soldiers had taken over their house in Beit Lahiya, had detained the men, who she said were farmers, and told the rest of the family to leave. The daughter was injured when the Israeli forces fired on the upper floors of the house before breaking the front door down.

Condemnation for the Israeli offensive grew across the Middle East.

Egyptian Foreign Minister Ahmed Abul Gheit said Israel’s incursion into Gaza came in “brazen defiance” of international calls to end the offensive, according to Agence France-Presse.

“The Security Council’s silence and its failure to take a decision to stop Israel’s aggression since it began was interpreted by Israel as a green light,” he said in a statement.

A State Department official said Saturday the United States was working toward a cease-fire, according to the Associated Press. But the White House has blamed Hamas for the escalating violence and blocked approval of a United Nations Security Council statement on a cease-fire.

The Israeli ground assault brings new risks and the prospect of many new casualties on both sides in a confrontation that, before this phase began late Saturday, had already cost the lives of more than 430 Palestinians and 4 Israelis.

While a ground war in densely populated Gaza is likely to increase the civilian toll there, the Israeli Army also faces new threats. Since seizing control of the territory a year and a half ago, Hamas has been able to smuggle in more and better weapons. Its more sophisticated arsenal has been on display in recent weeks, and even under heavy fire the group has shown its ability to keep hitting Israeli cities with long-range rockets.

Rockets fired from Gaza have plagued southern Israel for years, and they have drawn the military into the coastal territory repeatedly since troops formally withdrew and the Jewish settlements there were evacuated in 2005. A 48-hour raid in March 2008, aimed at inflicting a cost on Hamas for its continuing rocket fire, killed nearly 100 Palestinians.

Israeli officials have said repeatedly that it is not their aim now to fully reoccupy Gaza. But it was clear that the military expected a grueling operation.

“This will not be easy and it will not be short,” Defense Minister Ehud Barak said on national television shortly after the ground invasion began. He did not elaborate on how long Israel hoped to hold the rocket-launching sites.

The ground operation began after eight days of intensive attacks by Israeli air and naval forces on Hamas security installations, weapons stores and symbols of government in the Palestinian enclave. “This has always been a stage-by-stage process,” Shlomo Dror, a Defense Ministry spokesman, said in a telephone interview. “Hamas can stop it whenever it wants,” by stopping its rocket fire, he said.

Hamas leaders in Gaza were in hiding, but a Hamas spokesman said Saturday night by video that the “moment of decision has arrived” and that Gaza would be the Israeli Army’s “graveyard.”

Hamas has also threatened to use the invasion as an opportunity to capture Israeli soldiers. The group has been holding an Israeli corporal, Gilad Shalit, hostage for more than two years.

The exact number of troops entering Gaza was not being publicized, but the military said the operation involved “large numbers” of forces including infantry, tanks, engineering and artillery corps. On Saturday night, the Israeli prime minister’s office said that a call-up of thousands of army reserve troops, approved earlier, had begun.

Before Israel started the invasion, warplanes and ground artillery carried out heavy strikes on Saturday. Many of those attacks were on open areas around Beit Hanoun and the main route connecting the north and south of Gaza, most likely to clear those areas of mines and tunnels and to hamper movement before troops entered.

A mosque in northern Gaza was also hit, during evening prayer time, in what witnesses said was an Israeli airstrike. At least 11 worshipers were killed and about 30 wounded, according to Palestinian hospital officials. The Israeli military had no immediate comment.

The air force has struck several mosques in the past week, with the military saying they served as Hamas bases and weapons stores.

The Israeli Army also dropped thousands of leaflets into some residential districts warning inhabitants to evacuate their homes. Because of “the activity of terrorist groups,” the leaflets said in Arabic, the army “is obliged to respond quickly and work from inside your residential area.” Many residents of one apartment block in Gaza City said they had nowhere else to go and would stay in their homes.

An Egyptian-brokered truce between Israel and Hamas, which took effect last June, began to break down in November, and Hamas declared it over on Dec. 19. Since then, rocket fire out of Gaza has intensified.

On Saturday, a rocket hit an apartment building in the major port city of Ashdod, about 20 miles north of Gaza, lightly wounding two Israelis. Other rockets landed in the coastal city of Ashkelon and in the Negev Desert town of Netivot.

The latest round of rocket fire has demonstrated the extent to which Hamas has been able to upgrade its arsenal with weapons parts smuggled into Gaza, according to American and Israeli officials. Compared with the crude, homemade Qassam rockets it had used in the past, the latest rockets have been more accurate and have flown farther — close to two dozen miles, enough to reach the southern Israeli cities of Ashdod and Beersheba.

President Bush, in his weekly radio address to the nation on Saturday, said Hamas had instigated the violence last week with rocket barrages “that deliberately targeted innocent Israelis.”

Expressing concern about the humanitarian situation facing the people of Gaza, he added that the United States was “leading diplomatic efforts to achieve a meaningful cease-fire that is fully respected.”

President-elect Barack Obama continued to defer publicly to the Bush administration after the ground campaign began. “The president-elect is closely monitoring global events, including the situation in Gaza,” said Brooke Anderson, his chief national security spokeswoman. “There is one president at a time, and we intend to respect that.”

The United Nations Security Council held a closed meeting, called by France, on Saturday. Earlier, Secretary General Ban Ki-moon called for “an immediate end” to Israel’s ground operation, and asked Israel to “ensure the protection of civilians and that humanitarian assistance is able to reach those in need.”

Before the ground war began, hospital officials in Gaza City put the first week’s Palestinian death toll at more than 430, including 26 women, 74 children and an unknown number of male civilians. Three Israeli civilians and one soldier had been killed by rocket fire.

World reaction was intense and mixed. While thousands of protesters marched in cities across Europe to demand a halt to the Israeli bombing, in Prague, a spokesman for the new Czech presidency of the European Union said Israel’s actions were “defensive, not offensive.”

Other European countries quickly distanced themselves from the Czech position. The French Foreign Ministry condemned “the Israeli ground offensive against Gaza as it condemns the continuation of rocket firing.”

In London, the British foreign secretary, David Miliband, urged both sides to accept an immediate cease-fire.

More than 20,000 demonstrators marched against the Israeli air campaign in Paris and more than 10,000 in London, where some threw shoes at the prime minister’s residence, a particularly Arab form of protest that has gained worldwide currency since an Iraqi journalist hurled his shoes at President Bush last month in Baghdad.

Both protests were held before the ground invasion began. Large protests also took place in at least seven other European countries and in Kuwait, Israel and New York.

The Israeli military said Saturday evening that the air force had struck about 40 Hamas targets during the day, including weapons storage facilities, smuggling tunnels, rocket launchers and launching sites. Palestinians said the airstrikes also hit the American International School, a private institution in northern Gaza, killing a school guard.

Israel has also been firing on the homes of Hamas’s military leaders, and on Saturday struck a vehicle in Khan Yunis carrying Mohammed Maaruf, whom the Israeli military described as an officer in the Hamas ground forces. Another strike killed Mohammad al-Jammal, 40, who was said in Gaza to be a Hamas military commander, according to the news service Agence France-Presse. Israel said he was responsible for the entire rocket-launching operation in all of Gaza City.

A member of Hamas on Wednesday raised the group’s flag on the rubble of a mosque that was destroyed by Israeli warplanes in raids south of Gaza City.

Alongside the military offensive, officials said Israel would work with its allies to build a durable, long-term truce, and would seek to expedite and increase humanitarian aid. But it would not agree to a proposed 48-hour cease-fire.

Rather, the government said it would push ahead with its air, sea and ultimately ground operation, which one senior military official described as “making Hamas lose their will or lose their weapons.”

Strikes on Thursday morning hit government buildings as well as the Parliament, while in return militants in Gaza fired at least 13 rockets at locations in southern Israel, including two in the city of Beersheba, the Israeli army said. One relatively long-range rocket scored a direct hit on an eight-storey apartment house in the Israeli town of Ashdod, some 25 miles from Gaza, according to news reports. No injuries were reported and the Israeli Army said warplanes counter-attacked, hitting the site in Gaza from which the rocket was launched.

During days of aerial bombardment, Israeli warplanes have been destroying buildings once considered off limits, including mosques and government and university compounds, with officials asserting that rocket launchers and ammunition were made, stored and even operated from there. They were also hitting the homes of militants, smuggler tunnels and even money exchange shops to choke off Hamas from its suppliers.

The senior military official said that Gaza was limited in size and cut off from the outside and that Israel could win if it stopped future supplies and destroyed enough of what Hamas had. He added, however, that targets were running short, and that a limited ground operation aimed at destroying remaining sites was likely once the wet weather cleared.

Meanwhile, overwhelmed hospital officials in Gaza said that of the more than 390 people killed by Israeli fighter planes since Saturday, 38 were children and 25 women. The United Nations, which has estimated the number of dead to be between 320 and 390, said 25 percent of those killed were civilians. Israel said that it was still checking the numbers.

In the Jabalya Refugee Camp north of Gaza City on Wednesday, hundreds lined up for hours in the rain for bread and other staples as F-16 jets menaced overhead. At one point, two rockets were launched from within the camp — among about 60 shot into Israel on Wednesday — and an Israeli missile then hit the launcher.

The rockets that have been sent some 20 miles into the Israeli cities of Ashkelon, Ashdod and Beersheba in recent days are known as grads. They measure nine feet in length with warheads that weigh 30 to 40 pounds and were not manufactured in Gaza but were bought abroad and smuggled through tunnels from Egypt, Israeli officials said.

In Shifa Hospital in Gaza City, emergency personnel engaged in a brutal form of triage, allowing the worst cases to fade as they found themselves unable to cope.

A senior Israeli official said the country was seeking ways to increase humanitarian aid so that its military endeavor could continue without further pressure to stop. It permitted a dozen wounded and ill Gazans into Israel on Wednesday for treatment at hospitals here and allowed in some 100 trucks of food and medicine.

He also said that one limitation on the aid was that crossing points had come under attack by Hamas. A second, he said, is that donors are not bringing enough goods. Of the donations so far, some come from United Nations agencies, but most are from private donors.

Tens of thousands of Gazans have received recorded phone calls from the Israeli Army warning them that their houses have been marked as targets because they harbored either militants or weapons facilities like rocket workshops. Noncombatants were urged to clear out. Hundreds of thousands of leaflets gave the same message.

Israeli officials say their goals for a truce include a complete cessation of rocket and mortar fire from Gaza, a ban on armed men approaching the border with Israel, full Israeli control over the border crossings and a mechanism to ensure that Hamas is meeting its commitments.

The Hamas leader, Ismail Haniya, told Israel that there would be no talk of a truce until it ended its attack and all the crossings into Gaza from Israel as well as from Egypt were opened to full commercial traffic. He did not mention the rockets that Israel considers the central cause of its campaign.

On Thursday afternoon, Foreign Minister Tzipi Livni planned to meet in Paris with Foreign Minister Bernard Kouchner and President Nicolas Sarkozy, who are seeking ways to promote a cease-fire. From his ranch in Crawford, Tex., President Bush called Prime Minister Ehud Olmert. A White House spokesman, Gordon D. Johndroe, said Mr. Olmert had “assured President Bush that Israel is taking appropriate steps to avoid civilian casualties” in Gaza. In addition, he said, the Israeli leader told Mr. Bush that Israel was “targeting only Hamas operatives and those affiliated with Hamas.”

They discussed prospects for a cease-fire — “what steps could lead to a cessation of violence,” Mr. Johndroe said — but did not “get into specific timetables.”

“It all begins with Hamas agreeing to stop firing rockets” into Israel, Mr. Johndroe added. “The onus is on Hamas.”

The White House praised the diplomatic efforts of Egypt, Jordan and Saudi Arabia, but denounced Iran and Syria, saying they had supplied weapons to terrorist groups.

“Hamas is pretty well supplied by Iran and, to a certain extent, Syria,” Mr. Johndroe said. “Neither Iran nor Syria is playing a helpful role. They’re not playing a constructive role in this current crisis, which is pretty typical for their actions with regard to Hamas and Hezbollah.”

Israel’s Supreme Court told the government on Wednesday to allow foreign journalists limited access to Gaza, which had been closed to them since early November. The ruling, which urged the government to allow in a group of up to a dozen foreign journalists, came in response to a petition filed by the Foreign Press Association.

Mahmoud Abbas, the president of the Palestinian Authority, based in the West Bank, appealed to the United Nations Security Council for a cease-fire. Mr. Abbas, whose troops were forcibly ejected from Gaza by Hamas 18 months ago, is in a delicate position of not wishing Hamas to triumph but not wishing Palestinians to suffer.

In a speech delivered on Wednesday, Mr. Abbas reiterated that Hamas was responsible for the Israeli invasion because it ended the cease-fire between it and Israel 12 days ago. But he called what Israel was doing “the bloodiest massacre and systemic destruction of all forms of life; it is an aggression that does not target Gaza only but the entire Palestinian people and their cause and future and their most basic human rights.”

In the West Bank, the Palestinian police and security forces have had their leaves canceled. Some men associated with Hamas have been detained, and strict rules have been established for demonstrations in support of Gaza to avoid their turning into support for Hamas. Slogans and flags are limited, and close contact with Israeli forces and checkpoints has been barred to prevent trouble.

In Cairo, Arab countries appeared deeply divided over how to respond to the latest escalation in fighting between Israel and Hamas, with sharply differing comments from foreign ministers at the opening of an emergency Arab League meeting.

Moderate Arab states generally allied with the United States blamed Palestinian disunity for the crisis and more radical states, some of whom did not attend, urged collective action to defend the Palestinians against Israel.

In the most striking comments, Saudi Arabia’s foreign minister, Prince Saud al-Faisal, criticized the Palestinians for their inability to remain united behind President Abbas of Fatah — an implicit condemnation of Hamas, which took over Gaza entirely in 2007 in a brief but violent civil war with Fatah. Normally, during periods of Israeli-Palestinian fighting, Arab leaders condemn only Israel.

“This terrible massacre would not have happened if the Palestinian people were united behind one leadership, speaking in one voice,” Prince Saud said at the league meeting’s opening. “We are telling our Palestinian brothers that your Arab nation cannot extend a real helping hand if you don’t extend your own hands to each other with love.”

The three-day death toll surpassed 350, some 60 of them civilians, according to United Nations officials. Palestinian hospital officials reported that some 1,500 people were wounded.

Israel says that its onslaught — its most ferocious against Palestinians in decades — is designed to prevent Palestinians from attacking towns in southern Israel with missiles. But Hamas fired more than 60 rockets into southern Israel on Monday, killing an Israeli Arab construction worker in Ashkelon and wounding several others.

A long-range rocket also struck the Israeli city of Ashdod some 18 miles from Gaza, where it hit a bus stop, killing a woman and injuring two other people. Thousands of Israelis huddled in shelters.

The airstrikes followed bombing late Sunday that hit the Islamic University in Gaza, a Hamas stronghold, and the Interior Ministry, according to Hamas. Footage recorded from Israeli warplanes showed bombs striking the entrances to tunnels allegedly used to smuggle weapons into Gaza from Egypt.

The Hamas-owned television station Al Aqsa was also hit, as was a mosque that the Israeli military said was being used as a terrorist base. Speaking in Parliament, Mr. Barak said that the attack in Gaza would be “widened and deepened as is necessary” and referred to its operations as part of Israel’s long-term struggle against Israel’s Islamist enemies.

“Hamas is responsible for everything that happens in Gaza and which emanates from it,” Mr. Barak said.

The Bush administration placed the responsibility for ending the violence on Hamas.

“In order for the violence to stop, Hamas must stop firing rockets into Israel and agree to respect a sustainable and durable cease-fire,” a White House spokesman, Gordon D. Johndroe, told reporters in Texas. “Hamas has once again shown its true colors as a terrorist organization.”

But international calls for Israel to pull back intensified. At the United Nations, Secretary-General Ban Ki-moon again condemned Israel’s excessive use of force and called for an immediate cease-fire.

“The frightening nature of what is happening on the ground, in particular its effects on children, who are more than half the population, troubles me greatly,” he said. “I have continuously stressed the need for strict observance of international humanitarian law.”

In a statement on Monday, the Israeli Army said some areas around Gaza had been declared a closed military zone, a move which some analysts depicted as a potential precursor to a ground offensive. The military said the declaration meant that civilians, including journalists, could be denied access to an area up to two miles from Gaza.

The government on Sunday approved the emergency call-up of thousands of army reservists in preparation for a possible ground operation, as Israeli troops, tanks, armored personnel carriers and armored bulldozers massed at the border.

A military spokeswoman, Maj. Avital Leibovich, said the closed zone around Gaza had mostly to do with concerns of safety. She said the military had information that Hamas may employ either suicide bombers or more powerful missiles from the border area and it wanted to clear the area. She said she was sure journalists would be permitted to return.

“No one is trying to hide anything,” she said.

The continued airstrikes, which Israel said were in retaliation for sustained rocket fire from Gaza into its territory, unleashed a furious reaction across the Arab world, raising fears of greater instability in the region.

Much of the anger was also directed at Egypt, seen by Hamas and some nearby governments as having acceded to Israel’s military action by sealing its border with Gaza and forcing back many Palestinians at gunpoint who were trying to escape the destruction.

Witnesses at the Rafah border crossing described a chaotic scene as young men tried to force their way across into Egypt, amid sporadic exchanges of gunfire between Hamas and Egyptian forces. Egyptian state television reported that one Egyptian border guard was killed by a Hamas gunman. A Palestinian man was killed by an Egyptian guard near Rafah, Reuters reported. In Gaza, officials said medical services, stretched to the breaking point after 18 months of Israeli sanctions, were on the verge of collapse as they struggled to care for the wounded. At Shifa Hospital in Gaza City, women wailed as they searched for relatives among bodies that lay strewn on the hospital floor. One doctor said that given the dearth of facilities, not much could be done for the seriously wounded, and that it was “better to be brought in dead.”

Dr. Hussein Ashour, director of Shifa Hospital, said there were some 1,500 wounded distributed among Gaza’s nine hospitals with far too few intensive care units, equipped ambulances or dozens of other kinds of equipment.

The International Committee of the Red Cross appealed on Sunday for urgent humanitarian assistance, including medical supplies, to be allowed to enter Gaza. Some of the wounded were permitted to pass through the closed Rafah crossing to be treated at Egyptian hospitals on Monday, and the Egyptian government said it had sent 17 trucks to Gaza filled with medical supplies. Israeli officials said some aid had been allowed through one of the crossings from Israel.

Israel made a strong push to justify the attacks, saying it was forced into military action to defend its citizens. At the same time, the supreme religious leader of Iran and the leader of Hezbollah expressed strong support for Hamas.

Across Gaza, families huddled indoors as Israeli jets streaked overhead. Residents said that there were long blackouts and that they had no cooking gas. Some ventured out to receive bread rations at bakeries or to brave the streets to claim their dead at the hospitals. There were few mass funerals; rather, families buried the victims in small ceremonies.

At dusk on Sunday, Israeli fighter jets bombed over 40 tunnels along Gaza’s border with Egypt. The Israeli military said that the tunnels, on the Gaza side of the border, were used for smuggling weapons, explosives and fugitives. Gazans also use many of them to import consumer goods and fuel in order to get around the Israeli-imposed economic blockade.

While Israeli officials vowed to deal a critical blow to Hamas, Prime Minister Ehud Olmert said Israel’s goal was not to reoccupy Gaza, which it left unilaterally in 2005, but to “restore normal life and quiet to residents of the south” of Israel.

Tzipi Livni, Israel’s foreign minister, appeared on American talk shows to press Israel’s case. She said on “Fox News Sunday” that the operation “is needed in order to change the realities on the ground, and to give peace and quiet to the citizens in southern Israel.”

But in Damascus, Syria, a senior exiled Hamas official said that there can be no talk of a truce with Israel until the assault ends and Israel reopens the Gaza crossings.

“We need our liberty, we need our freedom and we need to be independent. If we don’t accomplish this objective, then we have to resist,” the official Abu Marzouk, told The Associated Press.

In Lebanon, the leader of the Shiite militant group Hezbollah, Sheik Hassan Nasrallah, put his fighters on alert, expressing strong support for Hamas and saying that he believed Israel might try to wage a two-front war, as it did in 2006. He called for a mass demonstration in Beirut on Monday. And he, too, denounced Egypt’s leaders. “If you don’t open the borders, you are accomplices in the killing,” he said in a televised speech.

Iran’s supreme religious leader, Ayatollah Ali Khamenei, condemned the silence of some Arab countries, which he said had prepared the grounds for the “catastrophe,” an Iranian news agency, ISNA, reported.

“The horrible crime of the Zionist regime in Gaza has once again revealed the bloodthirsty face of this regime from disguise,” he said in a statement. “But worse than this catastrophe is the encouraging silence of some Arab countries who claim to be Muslim,” he said, apparently in a reference to Egypt and Jordan.

Egypt has mediated talks between Israel and the Palestinians and between Hamas and Hamas’s rival, Fatah, leaving it open to criticism that it is too willing to work with Israel. In turn, Egypt and other Western-allied Sunni Arab nations are deeply opposed to Hezbollah and Hamas, which they see as extensions of Iran, their Shiite nemesis.

Across the region, the Israeli strikes were being broadcast in grisly detail almost continually on Arab satellite networks.

In the Syrian capital, Damascus, a large group of protesters marched to Yusuf al Azmeh Square, where they chanted slogans and burned Israeli and American flags.

In Beirut, protesters were bused to a rally outside the United Nations building, holding up Palestinian flags and Hamas banners. Muhammad Mazen Ibrahim, a 25-year-old Palestinian who lives in one of the refugee camps here, choked up when asked about the assault on Gaza.

“There’s an agreement between Egypt, Saudi Arabia, Jordan and Israel against Hamas,” he said. “They want to end them; all the countries are in league against Hamas, but God willing, we will win.”

That sentiment is widespread here. Many see Ms. Livni’s visit to Cairo last week as evidence that Egypt, eager to be rid of Hamas, had consented to the airstrikes.

The anger echoes what happened in July 2006, when the leaders of Saudi Arabia and Egypt publicly blamed Hezbollah for starting the conflict with Israel. Popular rage against Israel soon forced the leaders to change their positions.

Hamas, sworn to the destruction of Israel, took control of Gaza when it ousted Fatah last year. An Egyptian-brokered six-month truce between Israel and Hamas, always shaky, began to unravel in early November. It expired 10 days ago.

Palestinians emerged from the rubble following an Israeli missile strike in Rafah, southern Gaza Strip, Saturday.

Israeli military officials said the airstrikes, which went on into the night, were the start of what could be days or even months of an effort to force Hamas to end its rocket barrages into southern Israel. The operation could ultimately include ground forces, a senior Israeli security official said.

After the initial airstrikes, which Palestinian officials said also wounded at least 600, dozens of rockets struck southern Israel, where an emergency was declared. Thousands of Israelis hurried into bomb shelters amid the hail of rockets, including some longer-range models that reached farther north than ever before. One man was killed in the town of Netivot and four were wounded, one seriously.

A military operation against Hamas, the militant group that controls Gaza, had been forecast and demanded by Israeli officials for weeks, ever since a rocky cease-fire between Israel and Hamas fully collapsed a week ago, leading again to rocket attacks in large numbers against Israel and isolated Israeli operations here.

Still, there was a shocking quality to Saturday’s attacks that began in broad daylight, as police cadets were graduating, women were shopping at the outdoor market and children were emerging from school.

The center of Gaza City was a scene of chaotic horror, with rubble everywhere, sirens wailing, and women shrieking as dozens of mutilated bodies were laid out on the pavement and in the lobby of Shifa Hospital so that family members could identify them. Most of those killed were Hamas police officers and security men, including two senior commanders, according to Palestinian officials. But the dead included at least a dozen civilians, including several construction workers and at least two children in school uniforms.

The leader of Hamas in Gaza, Ismail Haniya, said in a statement that “Palestine has never witnessed an uglier massacre.” Later, in a televised speech, he vowed to fight Israel. “We say in all confidence that even if we are hung on the gallows or they make our blood flow in the streets or they tear our bodies apart, we will bow only before God and we will not abandon Palestine,” he said.

Plumes of dark smoke rose from Gaza City during the Israeli air strike.

By afternoon, shops were shuttered, funerals began and mourning tents were visible on nearly every major street of this densely populated city.

“We wanted to attack military targets while the terrorists were inside the facilities and before Hamas was able to get its rockets out that were stored in some of the targets,” said the top Israeli security official, briefing a group of reporters by telephone on condition of anonymity.

“Right now, we have to hit Hamas hard to stop the launching,” he added. “I don’t see any other way for Hamas to change its behavior. Hamas is not just a terrorist organization. It actually rules Gaza and is well supported by Iran with some of its leadership in Syria.”

A number of governments and international officials, including leaders of Russia, Egypt, the European Union and the United Nations, condemned Israel’s use of force and also called on Hamas to end the rocket fire.

The Bush administration blamed Hamas for the end to the cease-fire and demanded that it stop firing rockets, but called on Israel only to avoid hitting civilians as it attacked Hamas.

Ehud Barak, the Israeli defense minister and chairman of the Labor Party, said the military operation would expand and deepen as necessary, adding, “There is a time for calm and a time for fighting, and this is the time for fighting.” He said he was withdrawing from campaigning for Israel’s February elections to focus on the operation.

Hamas had in recent weeks let it be known that because of the coming elections it doubted Israel would engage in a major military undertaking. But in some ways the elections have made it impossible for officials like Mr. Barak not to react, because the public has grown anxious and angry over the rocket fire, which while causing no recent deaths and few injuries is deeply disturbing for those living near the Gaza border.

Israeli officials said that anyone linked to the Hamas security structure or government was fair game since Hamas was a terrorist group that sought Israel’s destruction. But with work here increasingly scarce because of an international embargo on Hamas, young men are tempted by the steady work of the police force without necessarily fully accepting the Hamas ideology. One of the biggest tolls on Saturday was at a police cadet graduation ceremony in which 15 were killed.  Spokesmen for Hamas officials, who have mostly gone underground, called on militants to seek revenge and fight to the last drop of blood. Several compared what was happening to the 2006 war between Israel and the Lebanese militia Hezbollah, when Israel reacted to the capture and killing of several soldiers along its northern border with air raids, followed by a ground attack. Hezbollah is widely viewed as having withstood those assaults and emerged much stronger politically.

The Arab League called an emergency meeting for Sunday in Cairo with all the foreign ministers from the member states.

Governments that dislike Hamas, like Egypt’s, Jordan’s and the Palestinian Authority in the West Bank, are in a delicate position. They blame Hamas for having taken over Gaza by force 18 months ago and oppose its rocket fire on Israeli towns and communities. But the sight of scores of Palestinians killed by Israeli warplanes outraged their citizens, and anti-Israel demonstrations broke out across the region. Egypt, worried about possible efforts by Palestinians to enter the country, has set up machine guns along the Gaza border.

In the West Bank and in some Arab parts of Jerusalem and Israel, Palestinians threw stones, causing some injuries. President Mahmoud Abbas of the Palestinian Authority angrily condemned the Israeli airstrikes.

Hamas is officially committed to Israel’s destruction, and when it won Palestinian legislative elections in 2006 and then forcibly took over Gaza in 2007, it said it would not recognize Israel, honor previous Palestinian Authority commitments to it or end its violence against Israelis.

Israel, backed by the United States, Europe, Egypt and the Palestinian Authority, has sought to isolate Hamas by squeezing Gaza economically, a policy that human rights groups condemn as collective punishment. Israel and Egypt, which control routes into and out of Gaza, have blocked nearly all but humanitarian aid from going in.

The result has been the near death of the Gazan economy. While enough food has gone in to avoid starvation, the level of suffering is very high and getting worse each week, especially in recent weeks as Israel closed the routes entirely for about 10 days in reaction to daily rocket fire.

Opening the routes to commerce was Hamas’s main goal in its cease-fire with Israel, just as ending the rocket fire was Israel’s central aim. But while rocket fire did go down drastically in the fall to 15 to 20 a month from hundreds a month, Israel said it would not permit trade to begin again because the rocket fire had not completely stopped and because Hamas continued to smuggle weapons from Egypt through desert tunnels. Hamas said this was a violation of the agreement, a sign of Israel’s real intentions and cause for further rocket fire.

On Wednesday, some 70 rockets hit Israel over 24 hours, in a distinct upsurge of intensity.

The rockets that flew into southern Israel on Saturday left the streets of cities like Netivot, a hardscrabble town of immigrants, nearly deserted. Inside a public shelter, parents worked to keep restless children occupied. The man killed by a rocket was hit by shrapnel as he stood in the entrance to his building, next door to where the rocket hit.

A victim of a strike on the Buriej refugee camp in Gaza. The attacks took place in broad daylight on about 100 sites.

Palestinians gathered at the site of a Hamas security compound in Rafah. A shaky Egyptian-brokered truce between Israel and Hamas started to break down in early November.

A member of the Hamas security fources was killed in the strike. "Hamas was warned a few times in a variety of ways, but I can't elaborate on the warnings," said Maj. Avital Leibovich, a spokeswoman for the Israeli military.