The talks, expected to take place at the Erez Crossing to the Gaza Strip on Tuesday evening, would be the first top level meeting between the sides since a Palestinian bomber killed five Israelis at a Tel Aviv nightclub late last month.
Israeli Prime Minister Ariel Sharon froze the handover of control of five West Bank cities - promised at an 8 February peace summit in Egypt - after the bombing and demanded that Abbas crack down on Palestinian militants first.
Israeli and Palestinian officials resumed talks in recent days as security cooperation improved and Abbas had five suspects arrested for the bombing, which was claimed by Islamic Jihad.
On Monday night, Palestinian and Israeli interior ministers met for the first time since the Tel Aviv bombing in what they termed a confidence-building measure, Aljazeera reported.
An Israeli security source said the withdrawal would not happen until after Tuesday evening's Abbas-Mofaz meeting.
Sharon's spokesman, Raanan Gissin, said on Sunday that the meeting would address "transferring security authority in the cities and improving security coordination which has been going pretty well in the past few days".
The cities to be handed over had been under Palestinian rule following a 1993 interim peace accord but were reoccupied by Israel during an uprising that erupted in September 2000.
Plans for a handover of security control of the desert town of Jericho were shelved in favour of Tulkaram after the sides failed to agree on the dismantlement of military checkpoints.
But a security source said there were no outstanding disputes over Tulkaram and that Abbas and Mofaz would set a date for the withdrawal, which could take place within hours of the meeting.