SHARM EL-SHEIK, Egypt - Israeli Prime Minister Ariel Sharon and Palestinian leader Mahmoud Abbas declared today that their people would stop all military or violent activity, pledging to break the four-year cycle of bloodshed and get peace talks back on track.

With the flags of their countries whipping in the wind, Sharon and Abbas met face-to-face at a Mideast summit today. 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 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.

Egyptian President Hosni Mubarak, who summoned the two leaders and has been a key mediator throughout the process, 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.

Mubarak also said there was now fresh hope for the Syrian-Lebanese peace track. Israeli-Syrian peace negotiations have been frozen since early 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.

In Jerusalem, a senior Israeli official said that Sharon had invited Abbas to his ranch in southern Israel, and the Palestinian leader accepted, a senior Israeli official said.Israeli Foreign Ministry official Gideon Meir did not say when the next Sharon-Abbas meeting would take place. Sharon owns Sycamore Ranch in southern Israel, near the Gaza Strip.Meir, who attended today's summit, 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.Top Sharon aide Raanan 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.Secretary of State Condoleezza Rice, speaking today during a visit to Rome, said there seems to be a will for peace in the Middle East, but warned the road ahead is long.Rice also urged the new Palestinian leadership to move resolutely to control violence against Israel by its own people. She acknowledged the limits of the Palestinian security forces, but said "there are places where they can act."She said when the Palestinian forces arrest someone, they should hold him, when they see a bombmaking facility they should destroy it and when they see smuggling they should stop it.In the hours before the summit began, the Israeli military said Palestinians opened fire on an Israeli military vehicle moving along the security fence surrounding the Gush Katif bloc of Jewish settlements in southern Gaza. No injuries or damage were reported. Israeli troops also arrested two Hamas members near the West Bank town of Jenin, the army said, adding that this arrest, like others in the past 10 days, was carried out with the specific approval of the army chief, Lt. Gen. Moshe Yaalon.Israelis also briefly sealed off the West Bank town of Nablus, preventing Palestinians from leaving.