The orders were issued simultaneously by Barak and Arafat, even as the death toll mounted in the disputed areas, during 10 hours of discussions in Paris with Secretary of State Madeleine Albright, said senior American mediator Dennis B. Ross.
The three areas are the Netzarim junction in northern Gaza, Joseph's Tomb in Nablus on the West Bank, and the Circle area of Ramallah, also on the West Bank.
The agreement marked a step toward reversing the confrontation between Israeli and Palestinian forces that has taken at least 65 lives and sidetracked already faltering peace talks.
Ross spoke to reporters as Albright flew to this Egyptian resort on the Red Sea for talks with Egyptian President Hosni Mubarak and Arafat.
Barak, meanwhile, flew home from Paris amid Israeli reports of a breakdown of efforts to defuse tensions.
"Both sides were very clear in terms of each trying to focus on key flash points, trying to avoid trouble in those areas, and effecting a separation in those areas," Ross said.
Albright said the Paris talks produced progress toward restoration of order. Barak and Arafat agreed to work to end the violence, she said, and CIA Director George Tenet will assist them. "The best thing here is to make sure there is calm," she said.
Barak and Arafat failed to agree on a formula for investigating the causes of the renewed fighting. Arafat wanted an international inquiry, while Barak preferred a joint Palestinian-Israeli probe, said a senior U.S. official, speaking on condition of anonymity.
The official called the talks productive, however, and credited both leaders with a sincere approach to restoring the trust essential for peacemaking to proceed.
Barak, for instance, agreed that Israeli forces would fire live ammunition only when their lives were threatened, the official said.
Mubarak, who has a reputation for evenhandedness and moderation, said he hoped wisdom and reason would prevail.
But, he said, "No peace can be durable if any party was coerced to surrender his rights and if Muslim sanctuaries in Jerusalem were undermined."
He spoke on the 27th anniversary of the 1973 war between Egypt and Israel.
Egyptian Foreign Minister Amr Moussa, angrily denouncing Israel for what he termed "the shooting of the children," called on Barak to prohibit all visits by Israeli officials to a key site in Jerusalem that is sacred to Muslims and Jews. Palestinian officials assert that the new wave of violence was set off by Likud leader Ariel Sharon's visit to the area Jews call the Temple Mount and Muslims know as Haram al-Sharif.
"Such a visit by Mr. Sharon should not happen again, by Sharon or any other official or nonofficial because of the seriousness of the situation," Moussa said.
At a joint news conference with Albright, Moussa said Barak should have attended the Sharm el-Sheik meeting. "What is going on in Jerusalem is unacceptable," he said.
Israeli Transportation Minister Amnon Lipkin-Shahak, one of the negotiators in Paris, had told Army radio in Israel earlier that Arafat had instructed his people in the field to stop the violence.
"It's a considerable step which could permit a return to calm, I hope with all my heart, in Gaza, the West Bank, and Jerusalem," French President Jacques Chirac said in Paris. "On the fundamentals, progress was made and measures drawn up aiming to a ceasing of the violence, which was obviously a precondition to the resumption of the necessary and inevitable peace process."
It wasn't clear how the shaky verbal agreements would translate on the ground. The Israeli army withdrew 23 tanks Wednesday from the outskirts of Nablus, a West Bank flash point, and planned to pull back additional tanks from outside the West Bank town of Ramallah on Thursday. Israeli officials said they were waiting to see if Arafat kept his commitments to contain the violence from the Palestinian side.
"I really hope that [both sides' promises] will be implemented today in the field, and then we will see things calm down in the field today," said Lipkin-Shahak.
Israeli forces came under sporadic fire in several locations in the West Bank and Gaza overnight, and small Jewish enclaves in Palestinian areas continued to be targets for attack. Palestinian gunmen fired in the direction of Jewish civilians and soldiers in the West Bank town of Hebron, where several hundred Jews live among more than 100,000 Palestinians.
An explosive device was thrown toward Joseph's Tomb, a tiny Jewish compound in the West Bank city of Nablus, but it failed to detonate, the army said.
The Paris talks were described as intense, and PLO official Laila Shaheed said Arafat stormed out--only to be stopped when Albright literally called guards to shut the residence's gates to block him.
Nabil Shaath, a top Arafat aide, said the Palestinian leader was angered by the Israeli and American refusal to set up an international inquiry into the recent bloodshed in Israel and the Palestinian areas.
U.N. Secretary-General Kofi Annan, who joined the talks late in the day, agreed to work with the Americans to devise a formula acceptable to both the Israelis and the Palestinians for such an investigation, a U.N. official said.
Barak's office has said he "totally rejected the call for an international investigation."
More than 1,800 people also have been injured in the past week, most of them Palestinians.
