The al-Aqsa Martyrs Brigade said on Saturday it was prepared to halt attacks through a mutual ceasefire.
This would come as a welcome boost for Abbas, who is seeking to persuade Israel of his ability to impose order in the territories.
However, the group set a strict raft of conditions on agreeing to a ceasefire, including that Israel announces a cessation of military operations, a halt to its policy of targeted assassination of resistance fighters and releases Palestinian prisoners.
Meanwhile, Abbas was to meet members of the Democratic Front for the Liberation of Palestine (DFLP) in his latest bid to ensure the new hope for a renewal of the Middle East peace process is not thwarted by resistance attacks.
Israel temporarily severed contacts with the Palestinian
Authority a week ago in the aftermath of an attack at Karni which killed six Israelis, an event that cast a huge shadow over Abbas's inauguration ceremony seven days ago.
However, contacts were resumed on the security level last
Wednesday, leading to an agreement for around 2500 Palestinian security forces to be deployed across Gaza in a move welcomed by Israel and the international community.