Prime Minister Ehud Olmert said on Tuesday he was determined to pursue Israel's offensive against Hizbollah as he met U.S. Secretary of State Condoleezza Rice to discuss the war in Lebanon.

US Secretary of State Condoleezza Rice salutes a US Marine as she walks towards a helicopter upon her departure from Beirut after meeting with Lebanese officials. Rice was to hold crisis talks with Israeli Prime Minister Ehud Olmert and Palestinian president Mahmud Abbas as part of a high-stakes mission to end the Middle East crisis, as deadly violence raged on in Lebanon.[AFP]

"We are using the basic elementary right of self-defence," Olmert said alongside Rice in remarks before they held talks.

Amid mounting international concern at civilian casualties, Rice met Lebanese leaders in bomb-battered Beirut on Monday.

She unveiled truce proposals there similar to Israel's demand for Hizbollah to pull back from the border to allow an international force to deploy, Lebanese politicians said.

"A durable solution will be one that strengthens the forces of peace and democracy in the region," Rice said with Olmert.

"It is time for a new Middle East. It is time to say to those who do not want a new Middle East that we will prevail."

On the battlefield, Israeli forces seized the key Hizbollah stronghold of Bint Jbeil inside southern Lebanon after fierce clashes with guerrillas in the town, Israel Radio reported.

Both an army spokesman and Hizbollah's Manar TV said fighting was still going on.

An Israeli air strike killed a family of seven, Lebanese security sources said. Hizbollah said five guerrillas died in the past two days. Israel reported two soldiers killed on Monday but said it had inflicted dozens of casualties on Hizbollah.

A total of 390 people in Lebanon and 41 Israelis have been killed in the conflict, ignited by Hizbollah's capture of two Israeli soldiers on July 12.

While saying she has no plan for Middle East shuttle diplomacy, Rice's schedule this week resembles just that. She arrived in Jerusalem after her trip to Beirut and will also visit Palestinian President Mahmoud Abbas in Ramallah.

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

Israel's army, which has also waged a military campaign in Gaza since June 28 to recover a soldier seized by Palestinian militants, believed it may have a week to keep pounding Hizbollah before a deal was reached, security sources said.

The heaviest fighting has been taking place around the town of Bint Jbeil. Israeli forces seized nearby another stronghold, the village of Maroun al-Ras, last week.

Among the issues on the table at Rice's meetings are U.S. demands Hizbollah withdraw away from Israel's border, the deployment of an international force alongside the Lebanese army in the area and the return of the Israeli soldiers.

Rice and Olmert were also expected to deal with 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.

Olmert said Israel was "very conscious" of the humanitarian needs of civilians in Lebanon.

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

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.

Prime Minister Fouad Siniora, who has pleaded for an immediate ceasefire, was more open to Rice's proposal and discussed ways of developing her ideas, his office said.

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

Many of the issues will be discussed at an international conference in Rome on Wednesday.

But ground 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.

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