Secretary of State Condoleezza Rice arrived back in Israel Saturday for another round of diplomacy to end more than two weeks of relentless fighting between Israel and Hezbollah militants in Lebanon.

Israeli Prime Minister Ehud Olmert, right, talks with U.S. Secretary of State Condoleezza Rice in Jerusalem

Secretary Rice is here for her second visit in less than a week. Her talks with Israeli and Lebanese officials are expected to focus on a framework to bring over two weeks of fighting to an end, and pave the way for a broader resolution of the conflict.

Israeli government spokesman Avi Pazner also said officials are eager to hear her proposals. "We want the attacks on Israel to cease. We want our soldiers freed. So, we are interested to hear Dr. Condoleezza Rice's ideas," he said.

An end to Hezbollah rocket attacks on Israel, as well as the release of two Israeli soldiers captured by Hezbollah July 12, remain Israel's most immediate conditions for stopping the conflict.

A longer-term demand and more difficult issue is the disarming of Hezbollah's militia, possibly integrating them into the Lebanese military, and then ensuring a national Lebanese army is deployed throughout the country.

There is widespread agreement an international force with a robust mandate will need to be sent to Lebanon to help in that process.

The Lebanese Cabinet, which includes Hezbollah loyalists, has backed Prime Minister Fouad Siniora's call for an immediate cease-fire and the deployment of an international force.

However, Hezbollah leader Sheikh Hassan Nasrallah has given that agreement only qualified support. Speaking on Hezbollah television, Nasrallah said Israel was being defeated on the ground. He dismissed Rice's diplomatic mission, and threatened more rocket attacks farther south into central Israel.

As diplomatic efforts rev up, the violence goes on. Israeli artillery continued to shell southern Lebanon, even though the military announced its troops had withdrawn from the fiercely fought over town of Bint Jbeil. Israeli air raids have been relentless, striking deep into eastern and southern Lebanon.

And, Hezbollah rocket attacks into Israel have not let up either, averaging about 100 a day.