Israel has pulled some of its troops from several neighborhoods in the West Bank. In Gaza, at least five people were injured when Palestinian protesters prevented police from arresting a leader of the Islamic militant group Hamas.
Israeli troops have started pulling out of some neighborhoods of the West Bank towns of Ramallah and Nablus. The moves come on the third-day of relative calm and amid signals of easing tensions.
Israeli and Palestinian security officials met overnight in their first face-to-face consultations since Yasser Arafat appealed Sunday for an end to militant attacks against Israelis.
Government advisor Zalman Shoval has said there is some promise of progress. He says Israel has offered to pull its troops out of Palestinian areas on a case-by-case basis.
"If they were to choose any of the Palestinian towns they wanted - up to them to decide which one - and to take care of the security situation in those towns, namely to arrest the terrorists and destroy the infrastructure and close the offices, etc. They could do this by their own volition, so to say, and we would not interfere. We would actually move out," he said.
Jibril Rajoub, who heads preventive security on the West Bank has said no progress was made in the meeting. He said the crackdown on militant violence is to enforce the cease-fire and is not dictated by Israel.
Mr. Shoval says only that Israel is waiting for an official response to its proposal.
Israel has demanded that Yasser Arafat crack down on extremist violence, but complains he is not doing enough. Mr. Arafat publicly appealed on Sunday for an end to militant attacks on Israelis. Mr. Shoval says Israel remains skeptical.
"The Israeli government has said very clearly - the Prime Minister and the Foreign Minister - that actions will have to speak, not words," he said.
There has been a lull in the violence since Mr. Arafat's speech, but earlier in the day Hamas supporters in Gaza prevented the police from arresting a key leader of the militant Islamic movement.
Mr. Arafat already has put Hamas' spiritual leader under house detention and closed down several Hamas offices in Gaza. But Hamas and other militant groups have rejected Mr. Arafat's appeal to end their attacks against Israeli civilians.