"The situation is deteriorating very gravely and if it does not come under control, it will be complicated and a third party, such as the Quartet, should intervene to stop the escalation of the events," chief Palestinian negotiator Saeb Erikat said on Wednesday after two hours of talks between Abbas and Egyptian President Hosni Mubarak.
The Quartet refers to the EU, UN, US and Russia, who back the road map peace plan for the Israelis and Palestinians.
Erikat said the two leaders discussed "the continued [Israeli] settlement activities, the ongoing building of the separation wall and the grave deterioration in the situation in Gaza".
Israel on Wednesday widened its five-day campaign against Palestinian fighters, firing artillery shells into the Gaza Strip for the first time and shutting down 15 West Bank offices suspected of distributing money to families of bombers from the Hamas and Islamic Jihad groups.
Israeli aircraft also fired missiles at several Gaza targets, knocking out power in Gaza City for most of the night.
In the West Bank, Israel rounded up 24 suspected fighters, bringing the number of people arrested since the weekend to more than 400.
Palestinian policemen also exchanged fire with armed men who approached the Gaza Strip's border with Israel on Wednesday, the first domestic clash since Israeli soldiers completed a pullout from the territory this month.
Witnesses said the armed men wounded two policemen and took at least one more hostage near Karni border crossing.
The identity of the armed men was not immediately clear, nor
their reason for approaching the border.
"The Palestinian Authority is fully committed to calm down the situation because it serves the supreme interests of the Palestinian people ... but the pledge should not come from one side and the Israeli side should stop its aggression and acts of violence," Erikat said.
Abbas later visited the headquarters of the Arab League, where he said Hamas was partly to blame for aggravating the situation in Gaza by insisting on celebrating the Israeli pullout on Friday and later refusing to admit fault in the explosion that took place, blaming Israel instead.
"The pledge [of ceasing hostilities] should not come from one side and the Israeli side should stop its aggression and acts of violence"
chief Palestinian negotiator
"Brothers in Hamas refused this talk and started firing missiles on the Israelis that made them say they did not have a partner in the peace process and started random attacks and bombing that destroyed many areas," Abbas told Arab League representatives.
Abbas said Hamas has the right to retaliate, but added: "We agreed in Cairo on a collective truce and the retaliation, therefore, should be collective too because this is an Israeli carnage, the result of which, must be shared by all parties."
Erikat said Abbas asked Mubarak to help the Palestinian Authority through Egypt's good relations with all parties, both internationally and regionally.
He also called on the Quartet to provide the mechanism for implementing the "road map" peace plan, including monitoring the situation on the ground.
In an interview with BBC Radio, Erikat said Mubarak had promised to make every effort to calm the situation and return the peace process to the right track.
On the final status negotiations Erikat said the Palestinian Authority believed that they should be resumed immediately to attain stability, peace and security for both sides.