Israel and Hamas held their fire on Monday as Egyptian and Palestinian officials contradicted Israel which denied it was brokering a comprehensive deal to end violence and lift the blockade of Gaza.
Palestinians said the two sides have made headway towards a truce, but Israel, while stressing the army would not hit Gaza if militants stopped firing rockets, insisted it was not negotiating a ceasefire.
"If the terror stops, if the Qassams stop landing ... Israel will have no reason to fight the terror organizations there... We will have no reason to retaliate," he said at a news conference.
Egyptian officials, supported by the United States, said they have been working on a deal.
"For the moment, we are at a preliminary stage over this; we are listening to all the parties so as to be able then to draw up a detailed and comprehensive initiative," said Mohammed Bassiuni, chairman of the Egyptian parliament's national security committee.
"With the developments in Egypt, I think there is an agreement in principle on that and a deal might be reached in the coming few days," said Abbas.
For a third day in a row, the Israeli army did not strike the Hamas-run territory and said Gaza fighters had all but halted their barrages, launching just one rocket and one mortar round since Sunday.
More than 130 Palestinians were killed in a broad Israeli offensive launched in late February to stop the rocket fire, raising concerns about the future of already faltering peace talks.
But efforts to bring about a ceasefire have gathered pace, with senior U.S. and Israeli envoys holding talks in Egypt over the past week, as have delegations from Hamas and Islamic Jihad.
"Period of calm"
Bassiuni, a former ambassador to Israel, told AFP the initiative would likely call for a "period of calm," an end of the Israeli blockade of Gaza and an exchange of prisoners between Israel and Hamas.
Hamas also said it was working with the Egyptians -- who have often played the role of Middle East mediator.
"(Hamas) will help the Egyptian leadership to reach a reciprocal and simultaneous truce that will at the same time lead to the lifting of the blockade imposed on the Palestinian people," said Ismail Haniya, who was prime minister in the Hamas-led unity government which Abbas fired after the Islamists seized Gaza in June.
Violence sharply escalated around Gaza sharply escalated in late February. In all, 133 Palestinians and five Israelis have been killed since.
Israel, the United States and the European Union view Hamas as a terrorist organization and have long sought to isolate the group.
But after Abbas said he was suspending peace talks in protest at the Gaza strikes, Washington encouraged Cairo to launch its mediation efforts.
"Israel today is in favor of a ceasefire with Hamas under certain conditions," a senior Israeli official told AFP.
Bassiuni said Israeli envoy Amos Gilad indicated during talks in Egypt that Israel was "ready for a lull" provided Hamas does not use it to smuggle in weapons from Egypt.