The militants' promise came after Israeli leaders said Sunday that Israel is ready to hold its fire if calm prevails, moving the two sides closer to ending four years of bloody conflict.

US envoy William Burns, a senior State Department official, is to arrive in the region later this week for talks with Israeli and Palestinian leaders on the emerging cease-fire deal. Abbas is seeking Israeli guarantees that it will halt military operations, including arrest raids and targeted killings of militants.

Israel in the past has refused to grant amnesty to militants, but appeared to be softening its position. Asaf Shariv, an adviser to Prime Minister Ariel Sharon, said Israel would not make public declarations. "It will be a de facto cease-fire," he said. "If there is quiet, we will respond with quiet."

Abbas on Monday was wrapping up a week of talks with militant leaders in Gaza.

Palestinian negotiator Ziad Abu Amr said the armed groups have promised to suspend attacks on Israel.

"They will continue doing that for some time to see if Israel is ready to accept demands and hold the truce," Abu Amr told the Voice of Palestinian radio, after Abbas said in a TV interview that he was close to sealing a cease-fire deal with the militant groups.