With the flags of their countries whipping in the wind, Sharon and Abbas met face-to-face at a Mideast summit Tuesday. Afterward, Abbas said: "We have agreed on halting all violent actions against Palestinians and Israelis wherever they are."
Sharon made a similar pledge.
"Today, in my meeting with chairman Abbas, we agreed that all Palestinians will stop all acts of violence against all Israelis everywhere, and, at the same time, Israel will cease all its military activity against all Palestinians everywhere," he said.
Abbas said he expected the cease-fire pledges to pave the way for resumption of talks on so-called "final status" issues such as borders, refugees and Jerusalem's status, all within the context of the Mideast "road map" to peace. Sharon said he also expected the deal Tuesday to set the stage for the implementation of the "road map."
During the summit, Sharon also invited Abbas to visit him at his ranch in southern Israel and Abbas accepted, according to a senior Israeli Foreign Ministry official, Gideon Meir.
Palestinian Foreign Minister Nabil Shaath said that meeting would take place soon.
Sharon said he would like the next meeting between the two leaders to be in the West Bank town of Ramallah, said his adviser, Raanan Gissin.
The Israeli flag was among those flying on the route from the Sharm el-Sheikh airport to the resort hotel where the summit was held, the Jerusalem Post reports. The last time Israeli and Palestinian leaders met there, in 2000, only the Jordanian, Egyptian, Palestinian and American flags were seen. At a summit in Aqaba in 2003, the Israeli flag was also absent.
An Israeli official said the presence of his country's flag showed a change in attitude.
Israelis and Palestinians are as hopeful as they were skeptical, reports CBS News Correspondent Robert Berger. There have been several other cease-fires in the past four years, and each one collapsed.
Abbas said it was time for the Palestinian people to regain their freedom.
"A new opportunity for peace is born today in the city of peace. Let's pledge to protect it," Abbas said, referring to the nickname of Sharm el-Sheik earned through past peace summits.
And Sharon, in what he said was a direct address to the Palestinian people, said: "I assure you that we have a genuine intention to respect your rights to live independently and in dignity. I have already said that Israel has no desire to continue to govern over you and control your fate."
Egyptian President Hosni Mubarak, who summoned the two leaders and has been a key mediator, said both sides showed a serious desire to "work together truly and sincerely."
"The challenges today are large and deep, but the mission is not impossible. If the road is long, we today took the first step," Mubarak said.
"The Palestinian and Israeli peoples equally deserve a secure life for the coming generations to enjoy, based on justice, international principles and good neighborliness," the Egyptian president added in a speech he said he was delivering on behalf of himself and Jordan's King Abdullah II.
Egyptian Foreign Minister Ahmed Aboul Gheit said Egypt and Jordan will return their ambassadors to Israel after a four-year absence, possibly within days.
Egypt and Jordan lowered their diplomatic representation in Israel in late 2000 in protest at what they saw as Israel's excessive use of force against Palestinians in the fighting that began in September that year. While Egypt withdrew its ambassador from Tel Aviv, Jordan decided not to send the ambassador it had newly appointed.
Mubarak also said there was fresh hope for the Syrian-Lebanese peace track. Israeli-Syrian peace negotiations have been frozen since 2000.
"Our goal is lasting peace in the Middle East, therefore, our movement will be followed by other moves to revive both the Syrian and Lebanese tracks," he said.
Meir said that "there was a great atmosphere in the talks ... smiles and joking."
An invitation to both sides to meet separately with President Bush at the White House this spring added momentum on the eve of the summit.
Gissin said that as part of Israel's halting of military operations, it would stop its controversial targeted killing operations against wanted Palestinians, as long as the Palestinians kept militants under control. Gissin noted Israeli flags, flying outside the summit convention center alongside the flags of Arab countries, calling it a sign of more hopeful times.
"But there's one thing that must be made very clear ... there will be no flexibility whatsoever, no compromise whatsoever on fighting terrorism," he said.
A Hamas spokesman in the Gaza Strip struck a cautionary note, saying the radical Islamic group, which has been responsible for hundreds of attacks against Israelis in the past four years, would evaluate the summit before committing itself to halting its campaign of violence.
"We agreed before with Mahmoud Abbas that if he succeeds to achieve our national goals, he should come back to the Palestinian factions to discuss the issue, and after that we will decide our stand," Mahmoud Zahar said.
The cease-fire was the clearest indication yet of momentum following Yasser Arafat's death, the election of Abbas and a signal from the White House that it plans a renewed push for peace.
Meanwhile, in Jerusalem, a key parliamentary committee narrowly approved a bill that would allow Sharon to carry out his planned pullout from the Gaza Strip and part of the West Bank in the summer. The vote passed 10-9 on a subject that has split Sharon's party and angered his main constituency — settlers and their supporters.