U.S. Secretary of State Condoleezza Rice met Tuesday with Israeli Prime Minister Ehud Olmert. Later Tuesday, Secretary Rice meets with Palestinian President Mahmoud Abbas. Both officials say there will be no return to the previous situation along the Lebanon-Israel border.

Secretary of State Condoleezza Rice, right, listens as Israeli Prime Minister Ehud Olmert makes statement to media before their meeting in Jerusalem, Tuesday

Broad agreement was evident between Condoleezza Rice and Ehud Olmert as they held talks in Jerusalem. Mr. Olmert says Israel is determined to keep fighting Hezbollah until it is no longer a threat.

"Israel is determined to carry on the fight against Hezbollah," he said. "We will reach out for them and stop them. And, we will not hesitate to take the most severe measures against those who are aiming thousands of rockets and missiles at innocent civilians for one purpose - to kill them."

Mr. Olmert describes Israel's offensive in Lebanon as "self-defense" and he urges Lebanon's government to distance itself from Hezbollah.

Both Israel and the United States say any cease-fire in Lebanon should not leave Hezbollah in place in southern Lebanon. Lebanon's government has asked for an immediate cease-fire, saying details of how to defuse tensions in southern Lebanon can be worked out later. Secretary Rice says any agreement to end the fighting should be durable.

"The people of this region, Israeli, Lebanese and Palestinian have lived too long in fear and in terror and in violence," she said. "A durable solution will be one that strengthens the forces of peace and democracy in the region."

Israel says it would support an international peacekeeping force to replace Hezbollah in south Lebanon, but, so far, no countries have offered to supply troops. The United States has ruled out participating in such a force and NATO officials say they have not received any request for troops. Other European countries, such as France, say talk of an international peacekeeping force is "premature."

U.N. officials say they are waiting for final approval from Israel to dispatch a humanitarian aid convoy from Beirut to south Lebanon. They say they are planning convoys for Wednesday and Friday. According to the United Nations, more than 700,000 Lebanese have been displaced by the fighting. Prime Minister Olmert acknowledges Israel's military operations have caused humanitarian problems for Lebanese civilians, saying Israel will work with the United States to try and alleviate the problems.

Israeli troops continue to encounter heavy resistance in their bid to capture the town, Bint Jbail, which they describe as a Hezbollah stronghold, about four kilometers inside Lebanese territory. Israel has been trying to capture the town for several days, saying it serves as a major supply and communications hub for Hezbollah in the area.