Jerusalem ? Spurred on by a U.S. peace mission, Israeli troops early today pulled out of Bethlehem, edging closer to a cease-fire with the Palestinians in the 18-month-old Mideast conflict.

The pullback came after Vice President Dick Cheney arrived to bolster the efforts of U.S. mediator Anthony Zinni, and the pair held talks Monday with Israeli Prime Minister Ariel Sharon.

In the most promising sign since Zinni arrived last week, Israel pulled back after midnight from the West Bank town of Bethlehem  traditional birthplace of Jesus  and neighboring Beit Jalla, El-Khader and the Aida refugee camp.

The Palestinians demanded at security talks Monday afternoon that Israel pull out of all their territory before a cease-fire could be declared.

Palestinian West Bank security chief Jibril Rajoub also told The Associated Press that the Israelis must declare an “immediate end to their aggression in all its forms, including house demolition, closures, and assassination,” and promise political negotiations as well as military talks.

Zinni, who has been shuttling between Israeli and Palestinian leaders, is trying to get the two sides to implement a cease-fire deal that CIA chief George Tenet brokered last year.

Both sides have previously endorsed the plan, which calls on the Israelis to pull back troops to the positions where they were before the fighting began in September 2000. The Palestinians must prevent attacks against Israel and collect weapons from militants.

Both sides see Cheney’s presence as an incentive to reach a truce deal.

Upon arriving, Cheney met Sharon and said he was seeking to revive Israeli-Palestinian talks with an aim to reaching a full-blown peace treaty based on U.N. resolutions. The vice president said both sides would have to make steps to end violence and improve the atmosphere for peace talks.

“We continue to call upon Chairman Arafat to live up to his commitment to renounce once and for all the use of violence as a political weapon and to observe a 100 percent effort to stamp out terrorists,” Cheney said.

“In that same spirit, I will be talking to Prime Minister Sharon about the steps that Israel can take to alleviate the devastating economic hardships being experienced by innocent Palestinian men, women and children,” he said.