The pair did not fix a firm date for the pullback but said it would depend on the outcome of further talks.
"In the coming days, we will apparently transfer two more cities after a meeting between military commanders tomorrow. We are talking about Tulkaram and Jericho," Mofaz told a news conference on Tuesday.
Abbas, speaking after meeting Mofaz, said: "The committees will begin working tomorrow. We have completed preparations with the Israeli side on the handover of Tulkaram.
"Tomorrow they will work on finalising preparations for handing over Jericho. They will withdraw from Jericho first."
A senior Palestinian official said differences still remained over the depth of a pullback from the two cities, and the military teams would try again to tackle the problem in their discussions.
"There are still problems, the same old problems, on whether the Israelis will remove checkpoints in those areas or not," the official said.
The talks at the Israel-Gaza border were the highest-level negotiations between the two sides since Abbas and Israeli Prime Minister Ariel Sharon declared a ceasefire at a summit in Egypt on 8 February.
"In the coming days, we will apparently transfer two more cities after a meeting between military commanders tomorrow. We are talking about Tulkaram and Jericho"
Israeli defence minister
Abbas went into the meeting after accusing Israel of undermining peace efforts by dragging its feet over promises to hand over Jericho, Tulkaram, Ram Allah, Bethlehem and Qalqilya to Palestinian security control.
Mofaz said he reaffirmed in his discussions with Abbas Israel's demand for the new Palestinian leader "to take the right steps to combat terror activities".
Since a bombing in Tel Aviv last month which killed five Israelis, Israel has stepped up calls for Abbas to crack down on resistance groups rather than try to coax them into halting attacks.
At the news conference at Erez, Abbas, elected on 9 January to replace the late Yasir Arafat, said the Palestinian Authority began to fulfil its security obligations two months ago.
"The Palestinian Authority is continuing to do so. It needs time and equipment," he said.
Mofaz (L) and Abbas failed to fix
a firm date for the withdrawal
Amid expectations the pullback would begin in the area around Tulkaram, Israeli officials said Mofaz wanted the army to leave positions outside Jericho first but that he would wait and see what Abbas preferred.
Plans for initiating the handover in Jericho, a centre of relative calm, were shelved in past weeks after the two sides failed to agree on the dismantling of military checkpoints.
"The talk is not only about cities, but about the areas surrounding those cities," Abbas said at the news conference.
"If there are checkpoints hindering movement, they should be removed," he added.
The five West Bank towns had been under Palestinian rule following a 1993 interim peace accord. But they were reoccupied after a Palestinian uprising that erupted in 2000.