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

Hamas until it renounces violence and recognizes Israel, though one Cabinet minister said Israel might consider outside mediation with the Islamic militants.

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 phone call to an Israeli TV reporter, said Hamas spokesman Taher Nunu. It followed a two-day air assault by Israeli forces that killed 12 Gaza militants, 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 militant 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 Islamic militant group has never agreed to those conditions.

On Tuesday, Olmert said the war against militants would not end and 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 militants, 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 has not approached his group about a cease-fire.

"This is not a time for truce," he told The Associated Press. "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 minimum essentials, and Egypt also shut its only crossing with Gaza. The result has been further hardship for the poverty-stricken territory.

Speaking at a sparsely attended Wednesday prayer gathering at a Gaza soccer stadium 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. "We greet it with tears in our eyes and sadness in our hearts."

The Eid al-Adha festival commemorates the ancient story of Abraham and his readiness to sacrifice his son, rendered in the Quran 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.

Outside their home in the upscale Gaza City neighborhood of Rimal, the Hamad family gathered to slaughter a cow after prayers, using a small crane to lift the 880-pound animal. One-third of the meat is traditionally distributed to the needy.

Although he paid 25 percent more for the cow than in the past, Alaa Hamad said he will give out more than the required third to poor neighbors. "Poverty now is a general phenomenon," he said.

Umm Ahmed Abu Assem, 50, said she had to sell her gold bracelet for $220 to buy her children a sheep to slaughter. "There is so much shortage as it is," she said.

People were trying to make do with what they have, substituting traditional feast staples with local goods. Chocolate has not been coming in, so strawberries_ abundant in the market because of an export ban — featured high in holiday handouts.