GAZA CITY, Gaza Strip - The Hamas-led Palestinian government called for a cease-fire in its violent two-week standoff with Israel but stopped short Saturday of offering to release an Israeli soldier held by Hamas militants. Israeli Prime Minister Ehud Olmert rejected the proposal by Palestinian Prime Minister Ismail Haniyeh.
Olmert will not agree to a truce until Hamas releases the soldier, officials in Olmert's office said.
Earlier, an Israeli Cabinet minister said Israel hopes the fighting, which has killed more than 40 Palestinians and an Israeli soldier, eventually will lead to a broader cease-fire deal.
In fighting Saturday, Israeli troops exchanged fire with Palestinian gunmen, and army bulldozers searched for militants' tunnels near Gaza City. In northern Gaza, tanks pulled out of the town of Beit Lahiya, leaving a wide swath of destruction after trying to carve out a buffer zone against rockets there.
Israel's two-week military campaign, prompted by the abduction of Cpl. Gilad Shalit has put the Hamas government under growing pressure. Israel has arrested several Palestinian Cabinet ministers and Hamas lawmakers.
On Saturday, Haniyeh issued a five-point cease-fire proposal, calling on Israel to halt its offensive and release prisoners but saying little about what Hamas is prepared to do in return.
"If we want to get out of the current crisis, it is necessary to return to calm, on the basis of a mutual halt to all military operations," said a statement issued by Cabinet spokesman Ghazi Hamad in Haniyeh's name.
Hamas also urged Israel to open negotiations over the fate of Shalit, 19.
However, Hamas often sends out conflicting signals, partly because of divisions between a more militant leadership in Syria and more pragmatic politicians in Gaza. Israel has largely held the Hamas political chief, Syrian-based Khaled Mashaal, responsible for the soldier's kidnapping.
Israel has said it would not engage in direct negotiations with the Islamic militant group, but Israeli officials said they were open to an Egyptian compromise proposal that would free Shalit without conditions and have Israel free some Palestinian prisoners later as a goodwill gesture.
Israeli Foreign Ministry spokesman Mark Regev said Hamas must release the soldier and halt rocket attacks on Israel as a first step.
"Anyone who ignores these two fundamental issues cannot hope to solve this crisis," he said.
Cabinet minister Ofir Pines-Paz said Israel hopes to go beyond those two immediate objectives and eventually negotiate a comprehensive truce.
"We have a great interest in changing the rules of the game," Pines-Paz, a member of the moderate Labor Party and of Israel's Security Cabinet, told Israel Radio.
"If we reach a situation in which there are no kidnappings, no rockets, no tunnels, no raids into our territory, certainly Israel will have to reciprocate."
The latest round of fighting, which claimed the lives of 35 Palestinians and an Israeli soldier over the past three days, began two weeks ago with a cross-border raid in which Hamas-allied militants seized the Israeli soldier and killed two of his comrades after sneaking through a tunnel.
Troops initially entered southern Gaza where Shalit is being held. Hamas said Friday he is being treated well, and a senior Israeli defense official, Amos Gilad, said Saturday that Israel also believes the soldier is alive.
On Saturday morning, dozens of tanks drove toward Gaza City, taking up positions about 500 yards from the outlying neighborhoods of Shajaiyeh and Zeitun. The army said forces were sent to the area to search for tunnels being dug by militants for possible attacks on soldiers.
The air force fired missiles at militants gathered at the outskirts of Shajaiyeh. Two Hamas gunmen were killed in the area, hospital officials said. Also, a Palestinian died of wounds sustained in earlier fighting.
The majority of the Palestinians killed since Thursday were gunmen, but one of the civilians killed was an 11-year-old boy.
Also, 65 U.S. citizens, many of Palestinian origin, left Gaza in a convoy escorted by U.S. consular officials. The visitors had asked to leave Gaza because of the fighting.
In northern Gaza, troops pulled back from Beit Lahiya on Saturday. Tanks driving through narrow streets had shorn off outer walls of buildings, torn down electricity polls, carved up asphalt. Facades of buildings were marked by bullet holes.
Bulldozers had torn up fields near homes, knocking down trees and greenhouses. As Palestinians picked through the wreckage Saturday, removing a dead goat from one heavily damaged dwelling, a U.N. truck arrived with drinking water.
Palestinian farmer Aref Sultan, 45, used the brief lull to move his wife and seven children, ages 2-16, to a relative's home further away from the fighting. Sultan said he and his family had been pinned down in their Beit Lahiya home during the past day.
"We went through 24 hours of terror," he said as the family loaded food and clothing into a pickup truck. "Shots were coming from all directions ... and the tanks were approaching our house. The children, and especially my 2-year-old son Samir, were screaming all the time."
Israeli military commentators have said it would be difficult for Israel to extract the soldier in a military operation. However, Israel also does not want to be seen as cutting a deal with Hamas.