The Palestinian and Israeli prime ministers are holding talks likely to set the tone for a three-way summit next week led by US President George W. Bush on taking the first steps charted by a peace "road map".
The two are meeting in Jerusalem where they are expected to discuss disagreements over the US-backed Mid East peace plan.
Prime Minister Mahmoud Abbas arrived at the Jerusalem office ofhis Israeli counterpart, for their second meeting in two weeks.
Ariel Sharon and Mahmoud Abbas are widely expected to strike a positive note in their meeting tonight to provide US President George W Bush with something concrete to justify his decision to get more personally involved in the region.
Raanan Gissin, a Sharon spokesman, said the Israeli leader approached the meeting with "guarded optimism". Palestinian Foreign Minister Nabil Shaath said: "We are going (into the talks) because we feel there is an opportunity."
Israeli officials said Sharon would renew an offer to Abbas to pull Israeli forces out of the northern Gaza Strip and a West Bank city, turning the territory into a proving ground for a crackdown on militants that could lead to further withdrawals.
Abbas spurned the proposal during his last meeting with Sharon on May 17, demanding that Israel first accept the US-backed peace plan calling for an immediate end to violence and reciprocal measures leading to a Palestinian state in 2005.
Israel endorsed the road map, the most ambitious peace initiative in the Middle East in two years, after the United States pledged to address the right-wing Sharon government's 14 reservations about the plan during its implementation.
But it remains to be seen which side will take the first step along a path to peace charted by the plan's sponsors: the United States, United Nations, European Union and Russia.
"I would think they (the Palestinians) are out of excuses," Israeli Immigration Minister Tzipi Livni said about accepting the withdrawal offer.
Shaath told Israel's Channel One television that Palestinian security forces needed time to rebuild after sweeping Israeli military operations during a 32-month-old uprising for statehood.
In an Israeli newspaper interview published hours before he met Sharon at the prime minister's office in Jerusalem, Abbas said he expected Hamas militants behind suicide bombings in Israel would agree to stop attacks on Israelis next week.
"Hamas will commit to halting terrorism both within the Green Line (inside Israel) and in the territories," Abbas, who is also known as Abu Mazen, told the Yedioth Ahronothdaily.
But Gissin said: "A ceasefire is not a substitute for taking real action to stop terrorist activity."
Hamas leaders said they were studying Abbas' proposal. His failure to secure a deal with Hamas in talks last week and militants' vows to wreck the peace plan raised doubts about his chances for success.
The al-Aqsa Martyrs Brigades, a militant group affiliated with the Fatah faction of President Yasser Arafat and Abbas, issued a statement in which it said it rejected "the road map to hell".
Israel has demanded the Palestinians begin disarming and arresting militants before it offers significant concessions.
The Palestinians want Israel to take steps of its own under the plan, such as uprooting Jewish settlement outposts built after March 2001 and freezing settlement expansion.
Abbas has made clear that he prefers negotiations to avoid sparking a Palestinian civil war. He took office on April 30 after Arafat bowed to international pressure to appoint a prime minister to initiate democratic and security reforms.