GAZA CITY, Gaza Strip – Palestinian Arabs and Israelis moved closer to halting more than four years of bloody violence yesterday, with the new Palestinian Arab leader saying he had made progress toward a truce deal with terrorists. Israel pledged for the first time to hold fire if calm prevails.

Palestinian Arab leader Mahmoud Abbas extended his stay in Gaza until today, trying to win a declaration from armed groups that they will halt attacks against Israelis. Mr. Abbas has been meeting representatives of Hamas, Islamic Jihad, and Al Aqsa Martyrs Brigade, a group with ties to his Fatah movement.

Israeli leaders said yesterday they would suspend their military operations if the Palestinian Arabs maintain calm, taking a major step in the direction of a cease-fire.

As in the past, the Palestinian Arabs were negotiating among themselves about conditions for halting violence without directly involving Israel – but making parallel demands on the Israelis.

A truce was not formally in place, but little violence was reported yesterday, as about 3,000 Palestinian Arab police patrolled Gaza areas near the Israeli border for a third day to prevent terrorists from firing rockets.

Though there have been other brief periods of quiet during four years of violence, optimism was heightened this time. Mr. Abbas – who succeeded Yasser Arafat after winning a January 9 election – was working around the clock to stop violence, backing up his earlier statements that violent Palestinian Arab resistance had been a mistake.

And on the Israeli side, Prime Minister Sharon was responding positively to Palestinian Arab moves for the first time, reflecting some confidence in Mr. Abbas, in stark contrast to Israel’s attitude toward Arafat. Mr. Abbas remained in Gaza yesterday, canceling plans to return to his West Bank headquarters in Ramallah. He told Palestinian TV that a truce accord was near.

“Everybody feels the responsibility and the importance of putting an end to the situation that we are all living in right now,” Abbas said. “We can say that there has been significant progress in the talks. Our differences have diminished, and therefore we are bound to reach an agreement very soon.”

Local officials of Islamic groups said an agreement has not yet been reached. Mr. Sharon convened his weekly Cabinet meeting in Sderot, a town outside Gaza that has been repeatedly targeted by Palestinian Arab rocket fire.

Mr. Sharon praised the recent calm as a “positive” development but warned of a tough response if attacks resume. “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,” Mr. Sharon said.

The defense minister, Shaul Mofaz, said that Israel wants to give the recently elected Mr. Abbas – also known as Abu Mazen – a chance to complete his cease-fire deal. “As long as there is quiet, there is no reason why we should act, certainly not while Abu Mazen is taking his first steps,” Mr. Mofaz told Israel Radio. In the past, Israel refused to promise the terrorists amnesty.

Mr. Mofaz, an ex-military chief and career officer, was uncharacteristically optimistic. “The year 2005 may be a turning point in which there will no longer be any soldiers in Gaza nor in the cities of Judea and Samaria,” he said, using the biblical name for the West Bank. Israel plans to pull out of Gaza in the summer.

Participants in the cease-fire talks have said a document being considered calls for the establishment of a Palestinian Arab state in the West Bank, Gaza Strip, and east Jerusalem, the areas Israel captured in the 1967 Middle East war.