In return, Israeli Prime Minister Ariel Sharon pledged Monday that he will continue attacking the violent Islamic Hamas, indicating that statements by President Bush have reinforced his resolve.
Sharon told the parliament his government would "pursue and catch every initiator of terrorism and its perpetrators in every place and at every time until victory."
Despite the tough statements by Hamas, Palestinian officials were optimistic that a deal can be announced very soon. "I hope we'll get some answers (from the militias) tomorrow," said Palestinian Foreign Minister Nabil Shaath.
Egyptian mediators summoned all Palestinian militias Monday in a final push to persuade them to halt attacks on Israelis.
"We are undergoing very serious negotiations with Hamas," said Palestinian Foreign Minister Nabil Shaath. "We'd like to see Hamas and other Palestinian factions commit themselves to a full cease-fire, leading to a full peace."
But after Monday's session, Ismail Abu Shanab, a Hamas leader, said it was premature to talk about a cease-fire. "Now is not a time for truce. It is time for solidarity and standing united against Israeli attacks on our people," he said.
The Egyptians told militia leaders they have American guarantees that Israel will halt targeted killings of Palestinians suspected of involvement in violence, participants in the talks said.
The armed groups have said they will only consider disarming if Israel promises to halt military strikes, including targeted killings. However, Sharon has said he would not make blanket promises.
After Monday's talks, an Egyptian diplomatic official said Egypt was seeking firmer guarantees from the United States, possibly in writing, that Israel will halt targeted killings. The mediators will report to Washington and the so-called Quartet of mediators on the meetings with the militants, the official said.
Officials at the U.S. Embassy in Tel Aviv declined comment on whether Washington has given such guarantees.
Aboard Air Force One, White House spokesman Ari Fleischer called Hamas an enemy to reform, to the Palestinian authority, and to the Palestinian people, who deserve a state, reports CBS News Correspondent Mark Knoller.
In a clear reference to Mr. Bush's statements calling for a world cutoff of funds to Hamas, Sharon said, "Because of our position, the voices against Hamas in the world are increasing, and there are calls to increase pressure on this murderous group. This is what we have done, and we will continue to do it."
Sharon repeated his offer of "painful concessions" for peace, without giving details, but added, "We will not give anything as long as the terror, violence and incitement continue."
Sharon told his Cabinet on Sunday that he would not initiate military strikes in the event of a cease-fire, but would continue targeting "ticking bombs," a term widely understood as referring to militants about to carry out attacks.
However, Israeli officials later said Sharon defines "ticking bombs" much more broadly and that it includes those who send bombers and other attackers. This would lower Israel's threshold for continuing with targeted killings.
There were conflicting reports on whether the Egyptians proposed an open-ended truce or a limited cease-fire for several months. Going into the talks, leaders of Palestinian factions said they are ready to consider halting attacks in Israel, but not in the West Bank and Gaza Strip. Such a partial truce would be unacceptable to Israel, the United States and Egypt.
The Egyptian mediators, assistants to Egyptian intelligence chief Omar Suleiman, held separate talks with various Palestinian factions, including Hamas, in Gaza on Sunday. On Monday, the mediators convened representatives of 13 factions.
Palestinian Prime Minister Mahmoud Abbas was to hold talks with the militia leaders in Gaza later Monday. Abbas has said that he would not use force to dismantle the groups, for fear of triggering a civil war.
Egypt has tried repeatedly in recent months to work out a truce, a so-called "hudna," but was rebuffed each time by Hamas, the largest and deadliest of the militias, whose lead the other armed groups have followed.
The latest talks come after a bloody week in which more than 60 people on both sides were killed in bombings, shootings and missile strikes, and Hamas threatened multiple attacks in retaliation for Israel's attempt to kill one of the group's leaders, Abdel Aziz Rantisi. He was wounded.
The United States is trying to salvage the road map, and intense U.S. and Egyptian pressure came to bear on Hamas after the surge in violence.
A senior U.S. State Department envoy, John Wolf, was to meet with Israeli officials later Monday to discuss the peace plan. Wolf heads a group of officials from the CIA and State Department who arrived over the weekend to supervise progress by both sides.