JERUSALEM, Israel – America will ask Israel to make “hard decisions” as it moves toward peace with the Palestinian Arabs, and both sides must live up to their promises, Condoleezza Rice said yesterday during her first trip to the Middle East as secretary of state.

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

Ms. Rice met privately yesterday with Prime Minister Sharon, the former warrior turned potential peacemaker. Today, she plans to visit with the Palestinian Arabs’ 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,” Ms. Rice said Sunday.

Ms. Rice did not go into specifics. But among the major challenges are what to do about Israeli outposts on land that Palestinian Arabs 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 Palestinian Arabs. In addition, the Palestinian Arabs hope to make east Jerusalem the capital of an independent state, while Israel claims the entire city as its capital.

Mr. Sharon greeted Ms. 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,” Mr. Sharon said in Hebrew.

In a boost to peace prospects, the mainstream Palestinian Arab movement Fatah said yesterday 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.

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

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

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

In Turkey earlier yesterday, Ms. Rice said America has no immediate plans to name a special envoy for Middle East peace, although the administration is working on ways to monitor or enforce a cease-fire.

Ms. 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.

Ms. Rice’s schedule is carefully laid out to balance Israeli and Palestinian Arab sensitivities. She will be the most senior American official to see Mr. 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 Arab leadership has embraced nonviolence, deployed police to keep the peace in Gaza, and won pledges from terrorists 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 Arab relations are improving dramatically ahead of the summit Tuesday.

Ms. Rice was to return to Europe today for meetings with Italian, French, and other leaders. Her stops there are helping pave the way for Mr. Bush’s own meetings with European and Russian heads of state later this month.

After her arrival from Turkey, Ms. 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 Mr. Sharon at her side later, Ms. 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,” Ms. Rice said.