The central committee of Abbas' Fatah movement also announced a state of emergency in the Palestinian security forces aimed at preventing new attacks.
Abbas is warning Islamic militant groups that further violations of the cease-fire with Israel will not be tolerated, reports CBS News Correspondent Robert Berger. Militants fired more than 50 mortars and rockets at Jewish settlements in Gaza yesterday, threatening the truce. Abbas responded by sacking three Gaza security chiefs. It's a major test for Abbas: If he cannot seize control of the streets from the militants, peace efforts will collapse.
Israel praised Abbas' swift action, but said it had only limited patience before it would take matters into its own hands.
Despite the renewed tension, Palestinian and Israeli officers met late Thursday at a Gaza crossing point to discuss cooperation. Israel Radio reported that the Israelis demanded a halt to the mortar and rocket fire, and the Palestinians spelled out their security plans.
In other developments:
As part of his efforts to end the violence, Abbas on Thursday fired Brig. Gen. Abdel Razek Majaidie, chief of public security, and police chief Saeb al-Ajed, security officials said. Abbas fired a total of nine officers, according to a statement from the Palestinian news agency.
He also headed to Gaza on Friday for talks with militant leaders. Cabinet Secretary Hassan Abu Libdeh said Abbas would "inform them that there is only one Palestinian Authority and one leadership, and (he) will not accept any measures that can subject our national project to danger."
Abu Libdeh emphasized, "The Palestinian Authority will not tolerate any actions that will sabotage the agreement reached with Israelis on a mutual cease-fire."
Hamas spokesman Sami Abu Zuhri said the talks would be held either Friday evening or Saturday.
Israeli analyst David Horovitz said Abbas needs to shift his strategy from persuasion to force.
"Negotiating with terrorists isn't going to work," Horovitz said. "You can't appease them, you have to take them on sooner or later. And that's really his test."
Israel's Deputy Defense Minister Zeev Boim warned Israeli patience wasn't infinite and the "window of opportunity is closing."
"We still have a policy of restraint and civil gestures in order to strengthen him (Abbas,) but it must be remembered this won't last forever. He has to take action," Boim told Israel Radio on Friday.
Palestinian lawmaker Ziad Abu Zayyad said Hamas was probably trying to strengthen its political position with the heavy bombardment. He said Israel must continue to show restraint.
"Israel has to refrain from any actions that could ignite the ground, that could be used as an excuse to torpedo the actions being taken by the Palestinian leadership," Abu Zayyad told Israel's Army Radio.
Abu Zuhri said Hamas was interested in a truce, but Israel needed to halt all raids against the militants and release prisoners in return.
"Hamas still wants a truce but needs this truce to be with Israeli obligations," he said.
Also Thursday, armed Palestinian stormed the main Palestinian Authority jail in Gaza and killed three prisoners, part of a clan feud. Abbas took that, as well, as an affront.
"These are very dangerous developments, and they violate the legitimacy of the Palestinian Authority," Abu Libdeh said. "No one can continue with these violations."
At a summit Tuesday in the Egyptian resort of Sharm el-Sheik, Israeli Prime Minister Ariel Sharon and Abbas declared an end to all violence and military operations.
In the wake of the barrages, Sharon's office called Egyptian, U.S. and Palestinian officials to express concern, and Defense Minister Shaul Mofaz warned, "If the Palestinians don't know how to deal with it, we shall do it."
Abbas has said all the Palestinian groups, including Hamas and Islamic Jihad, have signed on to the truce, but leaders of the two, responsible for dozens of suicide bombings that have killed hundreds of Israelis, deny that.
Up to now, Abbas has insisted he will not confront the militant groups and disarm them, as Israel and the internationally backed "road map" peace plan demand, preferring negotiations. However, he hinted that his patience has limits.
After a meeting late Thursday, the Fatah central committee announced a state of emergency and accused Hamas of violating the truce. "We are still committed to the language of dialogue, but at the same time, we warn against continuation of these irresponsible actions," according to a statement from the body.