The radical group Islamic Jihad said on Friday it would cease firing rockets at Israel if the Jewish state halted attacks on the Palestinians.
"The firing (of rockets) is a response to Zionist aggression," senior Islamic Jihad official Khaled al-Batsch told AFP as he was leaving a meeting with Palestinian president Mahmud Abbas in Gaza City.
"We are prepared to stop if their aggression ceases," he said.
Israeli planes have carried out raids against militants across Gaza since an Israeli mother of two was killed by a salvo of Palestinian rockets on Wednesday in the first such lethal attack from Gaza since July 2005.
Islamic Jihad was one of two groups that claimed responsibility for the deadly attack.
Although the Palestinian rockets rarely hit their target, they remain a constant nuisance to southern Israeli communities, and Israeli leaders have freely admitted they have no solution to the rocket threat.
In another sign of Palestinian efforts to calm the situation, prime minister Ismail Haniya of the Islamist movement Hamas said on Friday he saw "positive points" in the European initiative for an immediate cease-fire.
"On first viewing, this initiative has some positive points, but we are waiting to be informed officially so as to debate it and give an official response," he told journalists.
Spain, France and Italy pushed on Thursday for a new Middle East peace plan including an international conference, in a move welcomed by the Palestinian Authority but promptly rejected by Israel.
The initiative seeks a cease-fire, an exchange of Israeli and Palestinian prisoners, a Palestinian "government of national unity" and the despatch of a fact-finding mission to the Palestinian territories.
The UN General Assembly, meanwhile, was set to adopt an Arab-sponsored resolution slamming last week's Israeli killing of 19 Palestinians, mostly women and children, in the Gaza town of Beit Hanun.
In Israel, the head of parliament's foreign affairs committee, Tzahi Hanegbi, said such the European initiative would deprive the Jewish state of the ability "to strike terrorist infrastructure" in the Gaza Strip.
Also, it would allow militants "to capitalise on the calm to launch an armaments drive", he said, quoted by public radio.
Israeli Prime Minister Ehud Olmert has said he is opposed to a large Gaza offensive in retaliation for rocket attacks, which nearly five months of operations have already failed to stop.
"We should remember that this is not a war with a 'quick fix' solution," Olmert told reporters on his way home from the United States.
"Those who repeatedly mention 'Defensive Shield' (a huge 2002 operation in the West Bank) as an example, and demand that a similar operation be carried out in the Gaza Strip, must remember that terrorism has never ended," he added.
"I take the Qassam attacks seriously but our activities in Gaza will be carried out each time on the basis of intelligence, readiness and the ability to limit these attacks to the extent possible."
At a meeting with army chiefs in Tel Aviv on Wednesday, Defence Minister Amir Peretz ordered them to draw up new "aggressive" initiatives for Gaza.
Infrastructure Minister Benjamin Ben Eliezer has called for widened "targeted killing" operations, branded assassinations by the Palestinians, even warning that Haniya should not be immune.
Israeli forces first launched a massive military offensive against the Gaza Strip in late June, in a bid to recover the soldier seized by militants and to halt rocket attacks.
More than 300 Palestinians and three Israeli soldiers have since died in the territory, but rocket attacks continue and the conscript is still a captive.