The Palestinian prime minister said militants were prepared to stop firing rockets at Israel if it would halt all military action in Palestinian territories. Israel rejected the offer, saying it would respond positively only to a total truce.
Similar proposals in the past have failed to curb fighting, and a spokesman for the ruling Hamas group quickly stepped back from the cease-fire talk, which came as fighting between militants and Israeli troops in Gaza claimed the lives of a 10-year-old Palestinian boy and a militant filming the clashes.
A third Palestinian died on Friday of wounds sustained in earlier violence. It wasn't immediately known whether he was a militant or civilian.
Israeli launched a military campaign in Gaza five months ago, in an unsuccessful attempt to curb militant rocket fire on Israeli border communities.
Prime Minister Ismail Haniyeh of Hamas said armed factions had agreed on Thursday to halt rocket fire in exchange for a complete cessation of Israeli military operations in Gaza and the West Bank.
"The ball now is in the Israeli court," Haniyeh said.
"It [Israel] must stop its aggression and escalation against the Palestinian people, then there will be no problem according to what the factions agreed in their last meeting," he said.
After meeting with faction leaders again on Friday night, Haniyeh urged the Israelis "to respect this positive readiness expressed by the Palestinian resistance factions."
And government spokesman Ghazi Hamad suggested that a broader cease-fire was possible if Israel were to take up the militants' offer.
"After that, we [the Palestinians] will talk about a comprehensive truce," Hamad said.
Miri Eisin, a spokeswoman for Israeli Prime Minister Ehud Olmert, said the offer to trade a partial cease-fire for a suspension of all Israeli military operations in Palestinian territories was "ludicrous" and "a media stunt."
"Israel would respond very positively to the idea of a complete cease-fire in the Gaza Strip, which is what we hoped for in September 2005 when we left every inch of the Gaza Strip," Eisin said.
"If the Palestinian factions have a proposal which is supposed to bring about the complete stopping of fire from the Gaza Strip, Israel would be very happy to stop all, all -- and I'm going to say it again -- all fire from the Gaza Strip."
A Hamas spokesman in Gaza, Ismail Radwan, watered down Haniyeh's talk of a cease-fire, saying the Palestinian factions had agreed to "alter their strategies of resistance" if Israel halted fire.
The Palestinian rocket fire grew deadlier over the past week, claiming the lives of two Israeli civilians.
Eisin said Israel regarded efforts by moderate Palestinian President Mahmoud Abbas, to achieve a "complete stop of all violence" as a "very positive development."
Abbas has been trying to work out a package deal with Haniyeh that would include a total cease-fire and a more moderate government of professionals to replace the one led by Hamas, which doesn't recognize the Jewish state.
The two men met twice on Thursday, and aides to Abbas said the key sticking point in coalition talks was who would control the Interior Ministry, which is in charge of the Palestinian security branches.
Abbas hopes a more moderate government would encourage the West to restore vitally needed aid, cut off after Hamas took power in March. Western leaders have said the flow would not resume until the Palestinian government recognizes Israel and renounces violence.