In a news conference on Saturday, a masked al-Aqsa spokesman said the group would accept a ceasefire "if it is mutual and if Israel also commits to it". The spokesman was identified as Abu Muhammad.
Abu Muhammad said Israel must also agree to release Palestinian prisoners from its jails. "We think that all the factions, including Hamas and Islamic Jihad, believe that this ceasefire must be mutual," he said.
More than 7000 Palestinians are in prison for anti-Israeli activity, including violence. Israel has released small groups of prisoners in the past, but has balked at freeing those involved in deadly attacks.
Israeli officials said they were considering the proposal.
In the past, Israel refused to promise amnesty to resistance fighters, despite requests by Egyptian mediators who have said they could not seal a truce deal without such Israeli guarantees.
There have been thousands of
Palestinian casualties since 2001
However, two advisers to Prime Minister Ariel Sharon said on Saturday that a halt in Palestinian attacks could prompt the Israeli military to hold back.
"If there will be quiet on the Palestinian side, then there will be quiet on our side, because all of our military operations are only meant to stop terrorism," Zalman Shoval, a Sharon adviser, said.
Brigadier-General Giora Eiland, head of Israel's National Security Council, told Israel Radio that quiet would be met by quiet.
Deal to be finalised
The latest statements indicate that Abbas is making progress in his attempt to persuade armed groups to halt attacks on Israel.
Egypt has asked Palestinian officials and resistance leaders to come to Cairo in the coming days to finalise the deal, Palestinian officials said. The meeting would take place after the Muslim holiday of Eid al-Adha, which ends on Sunday.
In the past five days, Abbas has met repeatedly with representatives of the three key resistance groups, Hamas, Islamic Jihad and al-Aqsa Martyrs' Brigades. Abbas also held talks with smaller factions that are expected to fall in line if the larger three agree to a truce.
On Friday, some 3000 Palestinian police deployed in the northern Gaza Strip to prevent rocket and mortar fire on Israeli communities. No rockets have been fired since Wednesday.
On Saturday, there were only four shooting incidents in Gaza, the quietest day there since the outbreak of fighting in September 2000, a senior Israeli security official said on condition of anonymity.