On the 17th day of the war against Hamas, Israel said it launched around 15 airstrikes overnight, fewer than in some recent nights, as Israeli troops pushed into a heavily populated area of Gaza City from the south on Sunday in fierce fighting that reportedly continued on Monday.

Senior Israeli officials said for the first time in the war that they believed that the Hamas military wing was beginning to crack and that Hamas leaders inside Gaza were looking for a cease-fire. News reports said Hamas fired at least one missile out of Gaza into southern Israel without causing casualties.

The Israeli military said that warplanes attacked five Hamas operatives along with weapons caches, tunnels and other targets, while Israeli gunboats fired from the sea. Some of the airstrikes were called in by ground forces fighting Hamas gunmen, the military said in a statement.

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."

Blair was expected be in Cairo later on Monday, along with a senior Israeli Defense Ministry official, Amos Gilad. A Hamas delegation was 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.

Israeli officials 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. Israel began its military assault after a cease-fire agreement with Hamas expired, with a stated aim of silencing rocket fire by Hamas and other militants opposed to Israel's existence.

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, Major General 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."