An armed Palestinian group has said it would be prepared to accept a ceasefire if Israel agrees to stop attacks.
Mr Abbas hopes to strike a deal with militant groups by next week
The al-Aqsa Martyrs' Brigades would accept a truce "if it is mutual".
Palestinian leader Mahmoud Abbas has been holding talks with militant groups to urge them to halt attacks on Israel.
Al-Aqsa, which is linked to Mr Abbas' Fatah movement, demanded that Israel free Palestinian prisoners, halt military strikes and withdraw from Palestinian territories.
Mr Abbas is also trying to forge agreement on a joint political platform that would give him a stronger mandate in future negotiations with Israel.
At a news conference in Gaza City on Saturday, Al-Aqsa spokesman, Abu Mohammed, said: "We think that all the factions, including Hamas and Islamic Jihad believe that this ceasefire must be mutual."
The armed groups have said they want Israel to promise to stop military operations, including arrest raids and assassinations of wanted Palestinians.
Israel has refused to give such a guarantee in the past, and it remains unclear if it will do so now.
Al-Aqsa's announcement came a day after 3,000 Palestinian policemen were deployed in northern Gaza to halt rocket attacks on Israelis.
Israel praised Mr Abbas for his "positive action" in reining in militants.
Washington also gave an encouraging response to the Palestinian deployment.
"We have always stressed how important it is for the Palestinians to organize themselves to end the violence, and we welcome steps that are being taken in that direction," said state department spokesman Richard Boucher.
Assistant Secretary of State William Burns is due to visit the region next week to assess the possibility for re-starting peace talks.