Israel has proposed withdrawing troops from some Palestinian areas in the West Bank as a test case to see if Palestinian security can prevent attacks.
"We have no interest in staying in those places where the Palestinians can prove that they can take control," Israeli Foreign Minister Shimon Peres said.
The proposal was made at Israeli-Palestinian talks as part of an effort to find ways of easing the tough restrictions placed on Palestinians in the West Bank.
Israel's army has occupied seven of the eight main Palestinian cities and towns in the West Bank for the past month, keeping hundreds of thousands of Palestinians in their houses under a rolling curfew.
Mr Peres has not specified any areas, but Army Radio says the troops could withdraw from Hebron and Bethlehem as early as Tuesday if those areas remain quiet.
The Palestinians say their security forces can't re-establish control until after the Israeli forces pull out. Many Palestinian security force buildings have been damaged or destroyed by Israeli attacks on the structures.
"The key to breaking the circle of violence begins with the Israeli withdrawal from all the Palestinian cities," said Palestinian Information Minister Yasser Abed Rabbo.
The two sides plan to hold additional talks in coming days.