The United States will ask Israel to make "hard decisions" as it moves toward peace with the Palestinians, and both sides must live up to their promises, Condoleezza Rice (search) said Sunday during her first trip to the Middle East as secretary of state.

Rice's two-day visit to Israel and the West Bank headquarters of the newly elected Palestinian government is meant to nudge both sides to take hold of what Rice called "a time of opportunity" and end four years of war.

It comes as Israel backed off its long-standing refusal to release Palestinian prisoners accused of violence against Israelis and the Palesinian mainstream Fatah movement (search) declared it would be prepared for a cease-fire with Israel.

Rice met privately Sunday with Israeli Prime Minister Ariel Sharon (search), the former warrior turned potential peacemaker. On Monday, she planned to visit with the Palestinians' new president, Mahmoud Abbas.

"We will ask of our partners and our friends here in Israel that Israel continue to make the hard decisions that must be taken in order to promote peace and help the emergence of a democratic Palestinian state," Rice said Sunday.

Rice did not go into specifics. But among the major challenges are what to do about Israeli outposts on land that Palestinians eventually would control; the fate of the contentious separation barrier Israel is building between itself and the West Bank; and new security arrangements with the Palestinians. In addition, the Palestinians hope to make east Jerusalem the capital of an independent state, while Israel claims the entire city as its capital.

Sharon greeted Rice warmly, telling her in English, "you are among friends."

"Her visit, I believe, will contribute to the peace process that we so much want to advance," Sharon said in Hebrew.

Rice and Sharon later had a 90-minute dinner meeting, which State Department spokesman Richard Boucher said included a discussion of the initial steps from the new Palestinian government to end violence, and Israel's response.

Rice also outlined "a possible security mechanism to help Palestinians build effective security forces that fight terrorism and help Palestinians and Israelis in cooperating to end the violence."

Boucher did not give details, but the Bush administration is working on ways to monitor or enforce a cease-fire.

In a boost to peace prospects, the mainstream Palestinian movement Fatah said Sunday it would agree to a mutual cease-fire with Israel in the West Bank and Gaza. Fatah also ruled out attacks against civilians inside Israel.

Palestinians hope for such a mutual declaration when Abbas meets Sharon at a summit in Egypt. Rice is not attending that gathering.

Israeli officials said Sunday that top aides of Sharon and Abbas agreed late Saturday to form a committee to study additional Palestinian prioner releases, including of some involved in attacks on Israelis. Negotiators also made final an arrangement of conditional amnesty for Palestinian fugitives, they said.

A lasting peace deal for Israel and creation of a Palestinian democracy are chief foreign policy goals for the United States in President Bush's second term. For now, though, the United States is taking a low-key approach.

As Rice visited European capitals last week, she repeatedly said that Israel and the Palestinians should control their own path to peace, with help from the United States, Europeans and others.

In Turkey earlier Sunday, Rice said the United States has no immediate plans to name a special envoy for Middle East peace.

Rice is making an eight-day trip through Europe and the Middle East, her first overseas diplomacy since taking over from Colin Powell at the State Department.

Rice's schedule is carefully laid out to balance Israeli and Palestinian sensitivities. She will be the most senior U.S. official to see Abbas since his election last month. It is also the first time in years that a senior American official has gone to Ramallah, site of former Palestinian leader Yasser Arafat's crumbling compound.

Arafat's death in November invigorated the stalled peace process, and more hopeful signs followed.

The new Palestinian leadership has embraced nonviolence, deployed police to keep the peace in Gaza and won pledges from militants to halt attacks on Israel.

Israel has promised to release hundreds of prisoners, stop offensive military operations and gradually pull out of five West Bank towns.

While still characterized by great distrust, Israeli-Palestinian relations are improving dramatically ahead of the summit Tuesday.

Rice was to return to Europe on Monday for meetings with Italian, French and other leaders. Her stops them are helping pave the way for Bush's own meetings with European and Russian heads of state later this month.

After her arrival from Turkey, Rice stopped at Yad Vashem, the Israeli memorial for the 6 million Jews killed in the Nazi Holocaust of World War II. She laid a wreath and signed a memorial book.

She said her inscription read, "This is a place that causes all to remember those who perished and to accept that it must never happen again that good men and women do not act."

With Sharon at her side later, Rice smiled as she summed up the current situation.

"This is a hopeful time, but it is a time also of great responsibility for all of us to make certain that we act on the words that we speak," Rice said.