Hatim Abd al-Qadir, a member of Fatah's Supreme Committee, told Aljazeera from Jerusalem: "I believe there is an agreement now among all Palestinian factions on two main points.
"Firstly, to give the Palestinian Authority an opportunity to negotiate for Palestinian safety and security.
"Secondly, to ease the confrontation with Israel as an introduction to reach a long-term truce if Israel offers a positive commitment to cease its aggression by withdrawing from Palestinian land, releasing all political detainees and removing checkpoints."
Resistance - a right
"There are no guarantees for a truce so far," Abd al-Qadir said. "The truce is not a cancellation of the Palestinian resistance. Resistance is a major right of the Palestinian people," he added.
"We will work internally on downscaling operations against Israel," Abd al-Qadir said. "But if Israeli aggression and raids against our people continue, there will be no truce or ceasefire," he said.
"There are no guarantees for a truce so far. The truce is not a cancellation of the Palestinian resistance. Resistance is a major right of the Palestinian people"
Hatim Abd al-Qadir, member of Fatah's Supreme Committee
Senior Israeli officials meanwhile were divided over how to respond to Abbas' efforts to restore calm after four and a half years of an uprising sparked by Sharon's visit to the al-Aqsa mosque compound.
Abbas, who has been in Gaza since 18 January in an effort to persuade some of the resistance groups, such as Hamas and Islamic Jihad to negotiate, expressed confidence in a television interview on Sunday that an agreement could be reached soon.
Cooling down period
Both groups echoed his optimism on Monday as a key mediator in their talks said that an unofficial "cooling down" period was already in place.
Palestinian groups say they will
wait and see how Israel responds
"We have reached, in principal, agreement on important issues and the differences are very narrow," said Mushir al-Masri, a spokesman for Hamas.
"Everyone on the Palestinian side is determined to have a collective position," he added.
Abbas, elected president of the Palestinian Authority on 9 January, is seen as trying to persuade the groups to change strategy.
While both Hamas and Jihad boycotted the presidential contest, they have agreed to take part in July's legislative elections and in municipal polls that are to take place in Gaza this week.
Masri confirmed that the discussions with Abbas had focused on political participation, including the idea of Hamas joining the Palestine Liberation Organisation (PLO).
Nafaz Azzam, part of the Jihad delegation at the talks with Abbas, said there had been agreement on many core issues, while remaining differences could be ironed out later.
"Of course there can be no talk of a ceasefire without a price being paid by Israel"
Both groups were unequivocal, however, in their insistence that Israel must not sit on its hands.
"Of course there can be no talk of a ceasefire without a price being paid by Israel," Masri said.
"But if the conditions announced by Abu Mazin (Abbas) and the groups are met, then the movement will deal positively with the subject of the hudna (truce). These conditions represent a bottom line for the Palestinian people."
The resistance movements and Abbas are in agreement that Israel must release Palestinian detainees and end its military activities in the occupied territories.
Finance Minister Benjamin Netanyahu has argued that Israel should feel under no obligation to react with gestures to Palestinian groups.
He saw no reason for compromise by Israel.
"I don't see why Israel must give something," Netanyahu told Israeli army radio. "They [Palestinians] must give something."
Israeli response awaited
Israeli Deputy Prime Minister Shimon Peres struck a more conciliatory line, praising Abbas for his efforts.
Shimon Peres says Israel should
ease Palestinian living conditions
"Abu Mazin has made enormous efforts against terrorism but this does not signal that he has total control," Peres, leader of the centre-left Labour party, told army radio.
"I think that we must renew the dialogue with the Palestinians and try to ease their living conditions, particularly by lifting the roadblocks and withdrawing our troops from the cities in the West Bank if the Palestinian Authority wants to take over security," he added.
Ziad Abu Amr, a former Palestinian cabinet minister who is seen as playing an instrumental role at the truce talks, confirmed that the groups had agreed to a period of quiet while awaiting Israel's response.
"The Palestinian parties have agreed to calm the situation and we are waiting to see if Israel is ready to respond to that and then to hold a truce," he told Al-Quds newspaper.