At a meeting with Fatah’s top officials, Mr Abbas attempted to shore up his power base ahead of crucial talks with Hamas and other Palestinian factions in Gaza on Wednesday.
The groups are angry over Mr Abbas’s decision to delay July 17 legislative elections in Gaza, to allow time for an election law to be officially adopted.
Hamas spokesman Sami Abu Zuhri condemned the “unilateral decision” which he said “risks causing chaos”.
The militant group, which has seen its popularity grow, will be contesting legislative elections for the first time and is expected to gain substantial political clout in the Palestinian parliament.
The prospect of a Hamas victory has rung alarm bells with Fatah, which until now has dominated both the Palestinian Authority and the Palestinian parliament.
Palestinian officials have touted November as a possible date for the elections by which time Israel’s planned withdrawal from the territory should be complete.
Officials said a new date would be set following consultations with the various factions.
In the West Bank town of Nablus a group of militants from the al-Aqsa Martyrs’ Brigades, linked to Fatah, ambushed a government building and accused Mr Abbas of failing to honour security promises.
“We demand that the Palestinian Authority, especially Abu Mazen (Abbas), keeps their promises. He promised us jobs in the security services and that he would secure our safety. We have seen none of it,” the group said in a statement.
Meanwhile, The Bush administration is showing signs of easing its hardline approach toward Hamas.
The White House acceded to Hamas running candidates in Palestinian elections, even though it has refused to disarm and Washington lists it as a terrorist organisation.
US officials said they may be open to contacts with some Hamas political affiliates and left open the possibility of dealing with the group if it ended violence, in contrast to past calls for its total dismantlement.
A senior administration official said: “We’re not acquiescing. We do not deal with terrorists.” But he dded: “How do you pursue this without limiting democratic choices?”