The two leaders held talks over dinner on Saturday night and Rice did not speak publicly after the meeting.

Israel's popular Yedioth Ahronoth newspaper cited political sources as saying that the two leaders discussed the possibility of France and the Lebanese army taking part in a multinational peacekeeping force, which is expected to take position along the southern Lebanese border with Israel.

The conditions for the establishment of the international force,the length of its mandate and its responsibilities have not yet been finalized although Rice expressed optimism that it would be set up very soon, according to the report posted on the newspaper's website.

Paris has said that the international force should not be sent to Lebanon unless a ceasefire and a political deal are reached.Israel hopes the force can deter Hezbollah from reaching theborder area.

Meanwhile, Israel Radio reported that during the talks, Rice and Olmert also discussed humanitarian aid to Lebanon.Arriving in Jerusalem on Saturday evening, Rice embarked on a new round of diplomacy aimed at ending the conflict between Israeland Lebanon's Shiite group Hezbollah, which erupted more than two weeks ago following the capture of two Israeli soldiers by Hezbollah guerillas.

Rice is also expected to meet with other top Israeli officials on Sunday, including Foreign Minister Tzipi Livni and Defense Minister Amir Peretz.

Before talks with Olmert, Rice told reporters that she hoped an agreement on the main conditions for a ceasefire within the framework of a UN Security Council resolution would be tabled asearly as Wednesday.

"I expect the discussions to be difficult, but there will have to be give and take," she said. "I assume and have every reason to believe that leadership on both sides of this crisis would like to see it end."

It is Rice's second tour to the Middle East in a week. But her diplomatic efforts were snubbed by Hezbollah chief Hassan Nasrallah, who said earlier on Saturday that the top U.S.diplomat's return to the Mideast region was aimed to impose U.S.conditions on Lebanon to serve its new Middle East plan and serve Israel.

Nasrallah also accused Washington of blocking efforts to put an end to the conflict.

"The Israelis are ready to stop the aggression and those who insist on perusing this fight are the Americans," he said.

Over 450 Lebanese, most of them civilians and more than 50 Israelis including 18 civilians have been killed in the violence so far and Israel has rejected a UN call for a three-day truce to allow aid into south Lebanon, arguing that Israel has opened a humanitarian corridor to and from Lebanon.