Israel's leaders debated Monday how and when to bring their 17-day-old offensive in Gaza to an end, as battles continued to rage on the edge of Gaza City and as Israeli reservists flowed into the territory, ready for a possible deeper push into urban areas.

The moves came as negotiators in Cairo sought to reach a cease-fire agreement, hoping to put a halt to violence that medical officials in the Gaza Strip said has claimed the lives of more than 900 Palestinians, as many as half of them civilians. Thirteen Israelis have been killed, three of them civilians.

Speaking after a meeting with Egyptian President Hosni Mubarak, special Middle East envoy Tony Blair said that "the elements of an agreement" for a cease-fire were in place. But Israeli officials with knowledge of the talks said significant obstacles remained.

Hamas representatives were also in Cairo on Monday, conferring with Egyptian officials including intelligence chief Omar Suleiman. An Israeli Defense Ministry official, Amos Gilad, was negotiating with the Egyptians by phone Monday and was expected to travel to Cairo later in the week.

The talks in Egypt center on the question of how to keep Hamas from smuggling weapons across the Egypt-Gaza border. A senior Israeli official said Israel and Egypt are in basic agreement on a plan that would allow the European Union and the West Bank-based Palestinian Authority to share responsibility for monitoring the border and the crossing point at Rafah.

"We think the Egyptian position is very reasonable," the senior Israeli official said. Egypt has said that it is reluctant to have any international monitoring presence on its borders.

But the Israeli official said the Islamist Hamas movement is adamantly opposed to any deal that would permit the Palestinian Authority, which is led by the secular Fatah party, to return to Gaza. Hamas, which won 2006 Palestinian legislative elections, routed Fatah forces in June 2007 and has had control of Gaza ever since.

Hamas leader Ismail Haniyeh, speaking from an undisclosed location on the movement's television station, attempted Monday to rally supporters. "As we are in the middle of this crisis, we tell our people we, God willing, are closer to victory. All the blood that is being shed will not be in vain," Haniyeh said, while also acknowledging that the group is pursuing diplomacy. Hamas leaders in Gaza could not be reached for comment because they have gone into hiding.

If the negotiations in Cairo are successful, they could preempt an Israeli push into the strip's densely packed cities and refugee camps, where Hamas leaders are believed to have taken refuge. Israeli military officials allege that Hamas politicians are riding out the war in a bunker beneath Gaza City's main medical center, Shifa Hospital, in addition to other sites.

Any broadening of the Israeli operation would also be likely to include an effort to retake the area around the Egyptian border, known to Israelis as the Philadelphi corridor, military analysts say.

Israel pulled its troops and settlers out of Gaza in 2005 but continued to carry out raids in the coastal territory as Hamas and its allies used the strip to launch rockets at Israel. A six-month cease-fire expired in mid-December, followed by a barrage of rocket launches aimed at southern Israel. Israel began its military offensive with a surprise attack on Dec. 27.

On Monday, Israel carried out more than 60 airstrikes, continuing to bomb tunnels along the border, as well as homes of Hamas leaders. There was intense fighting reported around Gaza City as Israel tightened its cordon on Gaza's largest population center, home to 400,000 of Gaza's 1.5 million residents.

Officials and analysts say Israel's top three political leaders disagree over how the remainder of the war should play out. Prime Minister Ehud Olmert is said to favor an expansion, while Foreign Minister Tzipi Livni and Defense Minister Ehud Barak are believed to be more hesitant. Barak has aggressively pushed the talks in Egypt; Livni has said that Israel can soon declare victory and withdraw. The three run the country together and must achieve consensus before Israel can act.

Olmert spokesman Mark Regev acknowledged that Barak, Livni and Olmert don't always see eye-to-eye, but said they have agreed on the war's aims. "It's probably a very good thing that we don't have group-think at the top levels of the Israeli government," he said.

In an interview with Israel Radio on Monday, Livni said Israel had succeeded in proving to Hamas it is serious about deterrence.

"Israel is a country that reacts vigorously when its citizens are fired upon, which is a good thing," she said. "That is something that Hamas now understands, and that is how we are going to react in the future if they so much as dare fire one missile at Israel." Israel and the United States consider Hamas a terrorist organization.

Gabriel Sheffer, a political scientist at Hebrew University, said politics may play a role in the differing opinions among the three. In elections slated for Feb. 10, both Barak and Livni are hoping to succeed Olmert, who is stepping down under an ethics cloud. "If the number of Israeli casualties goes up, the effect on Barak and Livni will be very bad," he said. "Olmert has nothing to lose."

Sheffer said U.S. politics may also be a factor: Israel probably does not want to be fighting a war when President-elect Barack Obama is inaugurated next week, he said.

As international pressure to end the war has mounted, Obama has largely stayed out of the debate over whether Israel should be allowed to continue its offensive, while President Bush has staunchly backed the Jewish state. In his final news conference as president, Bush again asserted Israel's "right to defend herself" and called on Hamas to stop its rocket fire.

"There will not be a sustainable cease-fire if they continue firing rockets," he said. "I happen to believe the choice is Hamas's to make."

Hamas and its allies continued to fire rockets into southern Israel on Monday, launching more than 20. There were no reports of major injuries, and the number was significantly down from earlier in the war, when Hamas was launching 40 per day or more.

"The organization has lost much of its willingness to fight," said Shlomo Dror, spokesman for Israel's Defense Ministry. "It's much less than we anticipated."

Military analysts, however, have warned that Hamas could be saving its ammunition, with plans to launch urban warfare if Israeli troops push into Gaza's cities and camps.

Ahmed Qassim, a 30-year-old insurance salesman, said Hamas fighters had moved into densely populated parts of Gaza City in recent days and were using residential neighborhoods as bases for firing rockets. But he blamed Israel for the civilian casualties that result when the military strikes at those fighters. "The Israelis are so powerful and they have so much technology," he said. "They should be able to tell the difference between the resistance and civilians."

The Israeli military has not allowed foreign journalists into Gaza to work independently. But the military on Monday permitted a small group of reporters to travel with troops into the strip. A Reuters journalist reported from the outskirts of Gaza City that soldiers said they were meeting little resistance, but that they were pushing into urban centers to try to draw Palestinian fire.

"We are tightening the encirclement of the city," Brig. Eyal Eisenberg said, according to Reuters. "We are not static. We are careful to be constantly on the move."