"We hope to achieve an early end to this violence. ... That means that we have to help the parties establish conditions that will make it possible for an early cease-fire that, nonetheless, does not return us to the status quo," Rice said.

Among the items Rice is seeking is an international agreement on a United Nations-mandated multinational force that can provide stability in the region.

Details to be worked out include what the international force would look like, including whether the troops would be stationed all over Lebanon or just in the tense, Shiite-dominated south. Also under consideration is the role of Lebanese forces and whether international troops would secure Lebanon's ports and airports.

A U.S. official, speaking Friday on condition of anonymity because of the sensitive nature of the discussions, said other possible elements of a proposal for the ending the conflict included:

-Disarming Hezbollah and integrating the guerrilla force into the Lebanese army.

-Urging Hezbollah to return Israeli prisoners.

-Making a commitment to resolve the status of Chebaa Farms, a small piece of land held by Israel and claimed by Lebanon.

-Setting up a "no-go" buffer zone in southern Lebanon.

-Creating an international reconstruction plan for Lebanon.

Elements of the proposal were first reported Friday by ABC News.

After Rice's arrival in Jerusalem on Saturday evening, she was expected to meet with Israeli Prime Minister Ehud Olmert and Foreign Minister Tzipi Livni, according to a senior State Department official who requested anonymity.

President Bush, holding a news conference in Washington Friday with visiting British Prime Minister Tony Blair, announced Rice's return and said, "She will work with the leaders of Israel and Lebanon to seize this opportunity to achieve lasting peace and stability for both of their countries."

The United States, adopting a diplomatic stance that has not been embraced by most allies, has been insisting that any cease-fire must come with conditions to address long-standing regional disputes.

Nearly every U.S. ally - except Britain and Israel - has called for a quick truce to end the bloodshed, along with efforts to get more needed humanitarian supplies to the Lebanese. They believe the difficult work solving of old grievances between Hezbollah and Israel can come later.

Rice spent three days dashing to high-stakes meetings in Beirut, Jerusalem, the West Bank and Rome before traveling to Malaysia on Thursday for the long-planned conference of the Association of Southeast Asian Nations.

She got a warm welcome during her first stop in Israel. But she has faced a series of difficult sessions with world leaders elsewhere who take exception to the course the U.S. is charting in the conflict on the Lebanese-Israeli border.

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