Militant groups have agreed to suspend attacks as they near a formal truce deal with Palestinian leader Mahmoud Abbas (search) and await Israel's response, a senior Palestinian official said Monday.

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.

Israeli President Moshe Katsav (search), who holds a largely ceremonial post, called Abbas on Monday, Katsav's office said. The two leaders talked about the importance of working together for peace, a statement said.

U.S. envoy William Burns (search), 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 Israeli 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 Palestine radio, after Abbas said in a TV interview that he was close to sealing a cease-fire deal with the militant groups.

Palestinian officials said Abbas would not formally declare a truce until he has won Israeli guarantees.

Abbas has also reached an understanding with the militant groups Hamas (search) and Islamic Jihad (search) on the terms of their political participation. Abbas will regularly brief the leaders of the opposition groups in coming months, particularly on decisions regarding the planned Israeli withdrawal from the Gaza Strip this summer, negotiators said.

The militants have said they will participate in parliamentary elections in July, allowing for the first time a real measure of their political power.

No violence was reported Monday, as about 3,000 Palestinian police patrolled parts of Gaza near the Israeli border for a fourth day to prevent militants from firing rockets.

Sharon responded positively to Palestinian moves for the first time, reflecting some confidence in Abbas, in stark contrast to Israel's attitude to Abbas' predecessor, Yasser Arafat (search).

Sharon on Sunday praised the recent calm as a "positive" development but warned of a tough response if attacks resumed. "I hope that perhaps the quiet will continue and if not, then the army and security forces will continue to do whatever is necessary in order to remove the threat," Sharon said.

Israel's vice premier, Shimon Peres, said the Israel should help Abbas as much as possible in winning popular support for his policies.

"There are things we have to do, in everyone's opinion, such as removing the obstacle of the checkpoints," Peres told Israel Army Radio.

Peres also warned that Iran is trying to disrupt the emerging truce deal. Iranian-backed Lebanese Hezbollah (search) guerrillas have been funding some Palestinian militant groups in the past two years.

"Iran ... is the center of terrorism in the Middle East," Peres said.