"We agreed with Prime Minister Sharon to cease all acts of violence against Israel and the Palestinians everywhere," Abbas said after meetings at this Red Sea resort with Sharon, Egyptian President Hosni Mubarak and Jordan's King Abdullah II.
Sharon said immediately after Abbas' remarks: "Today, meeting with Chairman Abbas, we agreed that all Palestinians will stop acts of violence against all Israelis everywhere, and in parallel, Israel will cease all its military activity against all Palestinians anywhere."
Palestinian officials hailed the statements as a cease-fire accord, though no formal agreement was signed and - more significant - Abbas lacks an endorsement from Palestinian militant groups, including Hamas.
Hamas spokesmen in Beirut and Gaza said that the group would study the new declarations but that it was not automatically bound by them and could resume attacks against Israelis. But Egypt and senior officials of the Palestinian Authority were expected to press the militant groups to support Abbas.
Rather than speaking about an end to the four-year Palestinian uprising, Abbas and Sharon spoke, instead, of a new beginning. Left unsaid publicly was that the new opportunities were made possible by the death of Palestinian leader Yasser Arafat, whose name went unmentioned.
Relations between Israel and the Palestinians have rapidly improved since Arafat's death and Abbas' election last month as president of the Palestinian Authority.
Yesterday's meeting seemed a significant achievement for having occurred without disruptions. It marked the first time that Mubarak had agreed to meet Sharon as prime minister. Both Egypt and Jordan said their ambassadors would soon return to Israel, after a four year absence in protest of Israel's military measures against the uprising.
Sharon spokesman Raanan Gissin suggested that the understandings reached yesterday were firm commitments, even if the sides stopped short of issuing a joint declaration.
"The two statements are unilateral in character, which will end up in bilateral results," he said.
Sharon invited Abbas to his ranch in Israel's Negev desert, Gissin said, and he expressed hope that Abbas would invite Sharon to Ramallah, the West Bank city that is the de facto Palestinian capital.
The leaders put off the most divisive issues, such as future of Jewish settlements, Israel's barrier wall in the West Bank and the status of Palestinian refugees. The two sides also must reach agreement on how many and what kind of Palestinian prisoners Israel will release in coming weeks.
Israeli officials have said that quiet on the Palestinian side would be met with reciprocal quiet. Israeli troops have stopped offensive operations in Gaza and the West Bank; Israel's defense minister said last night that troops were in defensive positions to guard West Bank and Gaza settlements.
Palestinian police, meanwhile, are continuing to meet with Israeli army commanders to coordinate Israel's planned pullout of troops from West Bank cities. New joint committees are to set criteria for the release of prisoners by Israel and the possible return of dozens of exiled militants.
Aides described yesterday's meetings involving Sharon and Abbas as cordial and extending beyond their allotted times. Sharon and Abbas spent more than an hour together before joining the others in an ornate oval conference room in the Movenpick resort hotel.
Armed Egyptian paramilitary police, standing facing the desert, lined the roads. Egyptian state television repeatedly broadcast the leaders' arrivals and their handshakes.
Before breaking for a late lunch, Sharon, Abbas and Mubarak made their public statements as they sat evenly spaced around a large table; they seemed anything but relaxed as they read their texts. The leaders did not take questions from the news media.
Mubarak described the meetings as "open-minded."
"The Palestinian and Israeli people both equally deserve the life they dream of," he said. "It is a big task. Our hopes are even bigger."
With little evident emotion, Abbas, sitting opposite Sharon, spoke next: "What we agreed to today is on a new beginning to bridge the gaps between us. We could not solve all our issues today. But it is time for our people to enjoy peace and the right to a normal life. It is time to replace the gun and the bullets with a good and real dialogue."
Sharon praised Abbas for his election victory; he expressed optimism but also stressed that there was little time to waste.
"We must move forward cautiously," Sharon said. "There is a very fragile opportunity that the extremists want to exploit. They want to close the window of opportunity for use and allow our two peoples to drown in their blood. If we do not act now they may be successful in their scheme."
"There is only one answer to them: We must all announce here today that violence will not win, that violence will not be allowed to murder hope," he continued. "I have no intention of missing this opportunity because we must not let the new spirit, which grants our peoples hope, pass us by and leave us empty-handed."
Sharon mentioned his plan to withdraw Israeli forces from the Gaza Strip later this year and then addressed Palestinians:
"We in Israel have had to painfully wake up from our dreams, and we are determined to overcome all the obstacles which might stand in our path in order to realize the new chance which has been created. You, too, must prove that you have the strength and the courage to compromise, abandon unrealistic dreams and subdue the forces which oppose peace."
Senior Palestinian negotiator Saeb Erekat said the most important step was to restore the confidence and trust lost to years of hate and violence.
"What we need is to revive hope in the minds of Palestinians and Israelis that peace is doable," he said. "It will be difficult, to be sure. But if we honor our commitments and our agreements, there is a chance."