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 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.”

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.”