The Palestinian prime minister has pledged to resume talks with militant groups to persuade them to stop attacks on Israel.
Abu Mazen's pledge to end violence has angered militants
Mahmoud Abbas - better known as Abu Mazen - also insisted there was no alternative to continuing dialogue with Israel to reach the goal of a Palestinian state.
But representatives from Hamas said they had no intention yet of going back to the talks which they abandoned on Friday in anger at what they saw as too many concessions being given to Israel.
For its part, Israel appeared ready to start some of its obligations under the international peace plan known as the roadmap by removing some illegal outposts established on occupied land.
For us there is no alternative to dialogue
Palestinian Prime Minister
However as most of the sites to be demolished are uninhabited, it is thought unlikely that the move will assuage many Palestinians.
Abu Mazen said he wanted to resurrect talks with Hamas and other groups rather than confront them.
"For us there is no alternative to dialogue," he said, adding that he "will not force anyone to resume dialogue".
The BBC's diplomatic correspondent Barnaby Mason says there is doubt about whether Abu Mazen has the strength and backing to get the end to violence demanded by Israel and the Americans.
Abu Mazen was criticised for giving too much to Israel in statements made after last week's summit with US President George W Bush and Israeli Prime Minister Ariel Sharon in Aqaba, Jordan.
But on Monday, he again condemned Palestinian attacks, as well as action by Israel's armed forces.
Five Israelis and five Palestinians died in attacks in the West Bank and Gaza on Sunday which our correspondent says was a clear challenge to the Palestinian prime minister.
"The position of the government is to denounce both attacks," Abu Mazen said.
ROADMAP MAIN POINTS
Phase 1 (to May 2003): End to Palestinian violence; Palestinian political reform; Israeli withdrawal and freeze on settlement expansion; Palestinian elections
Phase 2: (June-Dec 2003) Creation of an independent Palestinian state; international conference and international monitoring of compliance with roadmap
Phase 3 (2004-2005): Second international conference; permanent status agreement and end of conflict; agreement on final borders, Jerusalem, refugees and settlements; Arab states to agree to peace deals with Israel
He said his role at Aqaba had been co-ordinated with Palestinian leader Yasser Arafat - though correspondents say Hamas had implicit support from Mr Arafat when it criticised the outcome.
Militants accused the prime minister of equating Palestinian violence with terrorism, rather than resistance to Israeli occupation.
They also said he failed to address the refugee issue at Aqaba as well as the question of Jerusalem, the city which is claimed by both Israelis and Palestinians as their undivided capital.
Reuters news agency reported that Hamas leaders meeting in Gaza to discuss the latest appeal by Abu Mazen saw no reason yet to resume talks.
Ismail Abu Shanab, a senior Hamas official, was quoted as saying: "He has not changed his attitude from Aqaba. Therefore the situation is unchanged regarding dialogue with Abu Mazen."
Israel is expected to announce later on Monday a list of unauthorised Jewish settlements due to be dismantled in accordance with the roadmap plan.
Although the plan envisages Israeli withdrawal from all settlements in the occupied Palestinian territories, Mr Sharon said at Aqaba only that outposts considered illegal by Israel would be dismantled.
The sites thought to be included on the list are mainly vacant structures
Out of more than 100 settlements, about 15 outposts are scheduled for demolition, Israeli sources have told the BBC's James Reynolds in Jerusalem.
The international community considers all the settlements on the occupied territories of Gaza and the West Bank as illegal.
But many have been built with at least implicit approval from the authorities, particularly since Mr Sharon took power.
The army is expected to negotiate with settlers but may start to dismantle the buildings even if there is no agreement.
A settler leader, Yehoshua Mor-Yosef, told the AFP news agency: "We won't lay a hand on [Israeli] soldiers. They're our brothers."
But he added: "If we are evacuated, we'll return the night after and establish 10 new outposts."