Israel has confirmed it is to pull troops out of Bethlehem and nearby Beit Jalla.
Security commanders from both sides are to meet on Sunday to discuss the West Bank withdrawal.
Soldiers had moved into the area to try and track down the killers of Israeli cabinet minister Mr Rehavam Ze’evi.
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A Palestinian gunman in Bethlehem
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The incursions have left 37 Palestinians dead and angered the US but failed to net the minister's killers.
US President George W Bush welcomed the move and urged Israel to complete the withdrawal.
Mr Bush called on Mr Yasser Arafat to "make a 100 per cent effort to reduce the violence," and for both sides to re-start the peace process.
In Gaza, Mr Arafat said he remained committed to a September 26th ceasefire and that he hoped peace talks could resume.
Israel's pullout offer came hours after Israeli forces killed three armed Palestinians who were trying to infiltrate a Jewish settlement in the Gaza Strip, the military said. Hamas said it was responsible for the attack.
The offer to leave Bethlehem and Beit Jalla was made during a three-hour meeting in Tel Aviv of Israeli and Palestinian security commanders and a US official.
The statement said: "It was decided that the (Israeli defence) forces would withdraw from Bethlehem and Beit Jalla on Saturday night. The Palestinian Authority will take upon itself the responsibility to retain the quiet in the area, if the army leaves."
AP