Speaking in Jerusalem ahead of the meeting he said, "Israel is determined to continue on in the fight against Hezbollah. We will ... stop them.

"We are using the basic elementary right of self-defence."

Rice said a ceasefire was needed in the region, but not at any price.

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

"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," she added.

Ceasefire conditions

Rice told Lebanese leaders on Monday that Hezbollah must return two captured Israeli soldiers and withdraw from Israel's border before there could be a ceasefire, Lebanese politicians said.

Washington is arguing that UN resolution 1559 and the Taif  Agreement, which ended the Lebanese civil war in 1990, need to be fulfilled.

Both documents call for the Lebanese government to exercise  full control over its territory, and the disarmament of militias -including Hezbollah.

Lebanese politicians want an immediate ceasefire before a long term deal, but Israel wants Hezbollah to leave the border area and free the captured soldiers without conditions.

Ground raids and air strikes have failed to stop around 1,200 rockets being fired into northern Israeli towns and cities, where they have killed 17 civilians so far.

Rice left Israel after the talks to meet Mahmoud Abbas, the Palestinian president, before she heads to an international conference in Rome on the conflict on Wednesday.

"I have no desire to be back in three weeks or three months or six months when once again extremists have decided to use their advantages to destabilise the region," she said.

Ramallah protest

More than 2,000 Palestinians took to the streets of Ramallah before Rice's visit to show support for Hezbollah and protest against US policies.

Humanitarian corridor

Israel says it would accept an international force, and several European Union nations have said they were ready to contribute.

"From the Rome conference we expect an economic plan for Lebanon, an aide package, and also and above all a signal that the situation has changed," Israeli foreign minister Tzipi Livni said on Tuesday.

Israel is not among the participants.

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

Israel's offensive in the Gaza Strip is also continuing to try to recover a soldier captured by Palestinian fighters and halt rocket fire.

Israeli forces have killed at least 121 Palestinians in the month since then.