GAZA CITY, Gaza City - On Islam's most important holiday, the leader of Gaza's Hamas government appealed yesterday for a cease-fire with Israel and said his people - battered by Israeli military strikes and international sanctions - were greeting this year's feast with "tears in our eyes."

A spokesman for Israeli Prime Minister Ehud Olmert said there could be no deals with Hamas until it renounces violence and recognizes Israel, though one cabinet minister said Israel might consider outside mediation with the Islamic extremists.

Israel and Hamas have never had direct contacts because of the group's violently anti-Israel ideology. But they have agreed to short truces negotiated by third parties.

The appeal from Ismail Haniyeh, who heads the Hamas government in Gaza, came in a call to an Israeli TV reporter, Hamas spokesman Taher Nunu said. It followed a two-day air assault by Israeli forces that killed 12 Gaza extremists, two from Hamas and 10 from Islamic Jihad.

Israel "should stop its attacks and siege," Nunu said. "Then a truce would be possible, and not unlikely."

Hamas officials said they were working with other groups to try to stop the rocket fire into Israel and also sent overtures to Israel through unidentified third parties.

Olmert's office would not confirm that such messages had arrived. His spokesman, Mark Regev, said there would be no negotiations until Hamas recognizes Israel, renounces violence and accepts existing peace agreements between Israel and the Palestinians. The group has never agreed to those conditions.

On Tuesday, Olmert said that the war against extremists would not end and that its leaders were in Israeli cross-hairs. "We will get all those who are responsible for firing rockets," he said.

Israel's president, Nobel Peace laureate Shimon Peres, released an unusually harsh statement opposing talks with Hamas. He called the Hamas overture "a pathetic attempt to deflect world attention away from the crimes of Hamas and Islamic Jihad."

But cabinet minister Shaul Mofaz, a former army chief and defense minister, took a more conciliatory view. In an interview on Israel Army Radio, he said Israel might consider indirect contacts with Hamas to end the fighting.

As long as rocket attacks persist, Israel will not "for even one hour" let up its attacks on Gaza extremists, Mofaz said. But "mediation is something we can think about," he added.

At least one other cabinet minister supports contacts with Hamas, but a clear majority, including Olmert, is opposed.

Islamic Jihad spokesman Abu Hamza said Hamas had not approached his group about a cease-fire. "This is not a time for truce," he said. "We have to inflict revenge upon this criminal enemy."

Israel's air assault was the most punishing since Hamas overran Gaza in June.

After the Hamas takeover, Israel closed the borders to all but essentials, and Egypt shut its only crossing with Gaza. The result has been further hardship for the poverty-stricken territory.

Speaking at a prayer gathering at a Gaza soccer stadium yesterday for the beginning of the Eid al-Adha festival, Haniyeh blamed Israel for the sour atmosphere, referring to Israel's latest air assault.

"The Palestinians greet the feast differently from the other Muslim nations - with martyrs, with members of resistance dying, because of the crimes of the Zionist occupation," he said.

The Eid al-Adha festival commemorates the ancient story of Abraham and his readiness to sacrifice his son, rendered in the Koran as Ishmael, as an act of obedience to God, who provided a lamb to be offered instead. Main features of the holiday are slaughtering animals and giving gifts, but both have been curtailed this year because of shortages caused by the tight cordon around Gaza.