Israeli troops pulled out of biblical Bethlehem and a neighboring village early Tuesday, witnesses said, edging Israel and the Palestinians closer to a cease-fire.

Soldiers dismantled rooftop positions, made of sandbags, lowering equipment to the ground, and armored personnel carriers and tanks rumbled along the main roads of Bethlehem and Beit Jalla into Israeli-controlled territory.

However, Israeli troops remained in the village of El-Khader, next to Bethlehem, and enforced a curfew in the Aida refugee camp adjacent to the West Bank town, traditional birthplace of Jesus.

The pullback came during a one-day visit by Vice President Dick Cheney, winding up a tour of the region that concentrated on the U.S.-led campaign against world terrorism. Concerned that Palestinian-Israeli violence would disrupt the effort, Cheney called on both sides to end their conflict.

Israel TV reported that the withdrawal from the Bethlehem area was accompanied by a Palestinian assurance that Palestinian police would prevent gunmen from firing from Beit Jalla across a narrow valley at a Jewish neighborhood in a disputed part of Jerusalem, claimed by both sides.

Israeli media reports noted that twice before, Israel said it had such assurances, but the gunfire resumed shortly after the withdrawals. Palestinians said earlier that the Israeli pullback would be unconditional.

In the Gaza Strip, Israeli tanks were pulling out of a narrow strip of farmland in the northern part of the territory, seized after Palestinians fired rockets at an Israeli town, Israeli media reported.

The Palestinians said there could be no cease-fire before Israel withdraws from all Palestinian territory, and U.S. envoy Anthony Zinni strongly backed that demand.

Zinni arrived Thursday with a goal of achieving a truce to end nearly 18 months of violence. after holding talks with Israeli Prime Minister Ariel Sharon and Palestinian leader Yasser Arafat, he convened meetings of security commanders from the two sides to discuss military arrangements for a cease-fire.

Zinni's blueprint is a truce plan worked out by CIA director George Tenet last year but never carried out. Among its main points are a total cessation of violence on all sides and withdrawal of Israeli forces to positions they held before the fighting began.

The Tenet formula leads into a staged plan toward restarting peace negotiations, contained in the recommendations of an international committee headed by former U.S. Sen. George Mitchell.