DAY 13, JERUSALEM, July 25 (Reuters) – U.S. Secretary of State Condoleezza Rice meets Israel’s Prime Minister Ehud Olmert on Tuesday for talks on the war in Lebanon with little immediate prospect of a ceasefire with Hizbollah guerrillas. On a stopover in Beirut, battered by two weeks of Israeli bombing, Rice put forward truce proposals similar to Israel’s own demand for Hizbollah to pull back from the border to allow an international force to deploy, Lebanese politicians said.

"Any peace is going to have to be based on enduring principles and not on temporary solutions," Rice told reporters in Jerusalem before dinner with Foreign Minister Tzipi Livni. Despite the diplomacy, Israeli forces battled Hizbollah in southern Lebanon and planes kept up daily air raids. At least 378 people in Lebanon and 41 Israelis have died in the conflict, ignited by Hizbollah’s capture of two soldiers on July 12.

While saying she has no plan for Middle East shuttle diplomacy, Rice’s schedule this week resembles just that. She headed to Jerusalem after a surprise visit to Beirut and will also visit Palestinian President Mahmoud Abbas in Ramallah. Among issues on the table are an international force for south Lebanon and getting Hizbollah to move back from the border as well as return the soldiers it seized in a cross-border raid.

Rice and Olmert’s talks will also deal with the question of what can be done to ease the suffering for civilians in Lebanon, which estimates almost one-fifth of its population has been displaced by Israeli bombing. Most of the dead are civilians.

The United States backs the idea of a humanitarian corridor to get help to the needy, an idea Israel says it could support.

"We did feel that Lebanon has been dealt a severe blow," said David Welch, Rice’s point man on the Middle East. "There’s a lot of concern about that."

STICKING POINTS

One of the key sticking points for a ceasefire is the sequence of events for a deal.

Lebanese Parliament Speaker Nabih Berri, an ally of Hizbollah and close to Syria, told Rice in Beirut a ceasefire should come first, followed by an exchange of prisoners and then discussion of other issues, a Lebanese political source said.

The office of Prime Minister Fouad Siniora, who has pleaded for an immediate ceasefire, said he was more open to Rice’s proposal and discussed ways of developing her ideas. A U.S. official said Siniora also wanted a prisoner exchange first.

Israel wants Hizbollah to leave the border area immediately and free the captured soldiers without conditions.

Rice has made clear she is not seeking a quick ceasefire and any solution should address the root causes of the conflict — for which Washington and Israel blame Hizbollah and its backers in Iran and Syria.

Many of the issues will be discussed at an international conference in Rome on Wednesday. Rice is then set to go to Malaysia for talks with Asian leaders before a possible return to the Middle East.

Israel’s army believes it may have a week to keep pounding Hizbollah before a deal is reached, security sources said.

Recent fighting was concentrated around Bint Jbeil, about 4 km (2.5 miles) inside Lebanon, target of one of several Israeli forays in search of Hizbollah fighters and rocket-launchers.

But raids and air strikes have failed to stop Hizbollah firing rockets into northern Israeli cities, where they have killed 17 civilians so far. More than 100 rockets fell on Monday, wounding at least 11 people.

Israel says it would accept an international force to dislodge Hizbollah guerrillas from the border and several European Union nations have said they were ready to contribute to a U.N. peace force.

But just as Hizbollah has fought Israeli attempts to drive it from the south, it would likely resist an international effort to do the same.

Rice is also set to meet Palestinian President Abbas on Tuesday.

Israel’s Lebanon offensive coincided with an Israeli push into the Gaza Strip to try to recover a soldier captured by Palestinian militants and halt rocket fire. Israeli forces have killed at least 121 Palestinians in the month since then.

Early on Tuesday, Israeli aircraft fired a missile at the home of a militant from the governing Islamist group Hamas, wounding seven people.