GAZA CITY, Gaza Strip -- Egyptian mediators asked Palestinian militants Sunday to halt attacks on Israel in an effort to rescue a U.S.-backed peace plan that foundered after more than a week of violence. Israel's prime minister suggested he might accept a limited truce.
Palestinian officials said there were expectations that the current cease-fire efforts might succeed where others had failed, despite militia leaders' renewed assertions they will not lay down their arms.
In Maine, President Bush said he was confident of eventual peace between the longtime enemies, with a Palestinian state existing in peace beside Israel.
After a weekend meeting between Israeli and Palestinian security officials, both sides said Israel was considering a gradual withdrawal from Bethlehem and parts of the Gaza Strip, leaving security to the forces of Palestinian Prime Minister Mahmoud Abbas and security chief Mohammed Dahlan.
Addressing a Cabinet meeting Sunday, Israeli Prime Minister Ariel Sharon said that if militants agree to a cease-fire, Israel would, for the most part, respect it.
"If no one fires on us, we will not return fire, except in cases of ticking bombs," a Cabinet official quoted Sharon as saying.
Until now, Sharon had rejected the truce idea out of hand, demanding an immediate crackdown on the militants, including arresting their leaders.
Hamas leaders targeted
However, Sharon's new comments appeared highly conditional. Until recently, the phrase "ticking bomb" defined a militant about to carry out an attack. Then the Israelis widened the definition after a botched effort to assassinate Hamas leader Abdel Aziz Rantisi last week, calling him a "ticking bomb." That indicated that even if Hamas agrees to a truce, its leaders might not be safe from Israeli strikes that could rekindle violence.
In a reflection of the unpredictable dynamic of the Mideast conflict, other hopeful signs emerged over the weekend for the so-called "road map" plan, which envisions an end to 32 months of violence and the creation of a Palestinian state by 2005.
In talks Saturday with Israeli Maj. Gen. Amos Gilad, Dahlan proposed that Israeli troops withdraw from large areas of Gaza to positions held before the outbreak of fighting in September 2000. He asked Israel to pull out of the West Bank towns of Bethlehem and Ramallah, the Palestinians' administrative center.
Israeli Defense Minister Shaul Mofaz said Sunday he is considering a withdrawal from Bethlehem and parts of Gaza and said meetings with the Palestinians would continue.
In a first phase, Israel would pull out of the northern Gaza towns of Beit Hanoun and Beit Lahiya. Despite the talks, Israeli forces entered Beit Hanoun early Sunday, setting off a firefight that killed one Palestinian and wounded seven, doctors said.
And U.S. officials, underscoring their nation's commitment to the peace plan, arrived in the region to monitor its implementation.
The two Egyptian mediators, assistants to Egyptian intelligence chief Omar Suleiman, arrived in Gaza City on Sunday for cease-fire talks with Palestinian militants, most importantly with the group Hamas. They held a preliminary meeting with top members of Abbas' mainstream Fatah movement Sunday afternoon; Fatah also has carried out attacks, despite Abbas' call for them to stop.
Zakaria al-Agha, a senior Fatah leader, said a meeting with all Palestinian groups was planned for today.
"I am optimistic that all the Palestinian factions will work together," he said after Sunday's meeting.
The mediators then went for talks at Hamas founder Sheik Ahmed Yassin's house.
Afterward, Hamas spokesman Ismail Abu Shanab read a statement saying Hamas would consider some Egyptian proposals, but he did not give details or take questions.
"The Egyptians offered ideas supporting the Palestinian National Cause," he said. "We promised to study the ideas and give them an answer soon."
The Egyptians left without speaking to journalists.
The renewed violence came after a bloody week in which dozens were killed on both sides in bombings, shootings and missile attacks.
The violence also spurred intense U.S. mediation to rescue the peace plan, which Bush launched at a June 4 summit in Aqaba, Jordan, with Abbas and Sharon.
Bush said Sunday the world must deal harshly with Hamas and other militant groups that he said were trying to sabotage the peace process. He added: "I'm confident we can achieve peace. It's going to be a tough road, but I am determined to continue to lend the weight of this government to advance peace."
Dov Weisglass, a top Sharon aide, meets U.S. national security adviser Condoleezza Rice today in Washington. Secretary of State Colin Powell and other senior representatives of the road map sponsors -- the United States, United Nations, Russia and the European Union -- plan to meet Thursday in Jordan.
U.S. Assistant Secretary of State John Wolf, leading a team of American officials in the region to supervise implementation of the road map, will meet with Israeli officials today and with Dahlan and Abbas on Tuesday, Israel Radio said.
The road map plan calls for Abbas to dismantle militant groups. Israel has demanded a crackdown, but Abbas said he preferred to negotiate a cease-fire, fearing a crackdown would lead to civil war.
Truce talks broke up a week ago, but Palestinian officials said they were optimistic an agreement could be reached. Palestinian Information Minister Nabil Amr quoted an Abbas envoy to the talks as saying progress had been made.
However, for now the Palestinian factions propose at best to halt attacks in Israel, but not in the West Bank and Gaza, al-Agha said.
Hamas officials in Gaza have been most vocal in rejecting a truce, particularly after Israel tried to kill Rantisi last week. A 7-year-old girl wounded in that air attack died Sunday.
Sources close to the talks said Hamas leaders abroad are willing to consider a comprehensive cease-fire, provided Israel promises to halt targeted killings, incursions and other military strikes.
In other developments Sunday:
-- Israel said two British bombers sent to blow up a Tel Aviv bar on April 30 were sent by Hamas. Three Israelis were killed when one of the bombers blew himself up. The other escaped and was found dead several days later. Until now, no link had been made between them and a local group, and Hamas did not claim responsibility.
-- The Israeli settlement watchdog group Peace Now said settlers have established four more outposts in the West Bank in recent days after the military last week dismantled 10 such enclaves, in line with the road map.
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