JERUSALEM - Secretary of State Condoleezza Rice met with top Israeli officials on Sunday to try to iron out a cease-fire and a deeper political solution to underlying disputes with Lebanon that have long vexed Middle East leaders and exacerbated nearly a month of fighting.

While acknowledging the difficultly of ending three weeks of fighting between Israel and Lebanese-based Hezbollah militias, Rice hoped to clear the way for a U.N. resolution that would put in place an international peacekeeping force.

Asked Sunday morning whether she was any closer to getting a peace deal, Rice only smiled and said "Good morning."

Rice had dinner Saturday with Israel's prime minister, Ehud Olmert. She had breakfast Sunday with Foreign Minister Tzipi Livni and later met with Defense Minister Amir Peretz.

Rice hopes a resolution to help end the fighting could be ready to go to the United Nations Security Council by midweek, but won't put a deadline on completing that work. Israel Radio said the government would not agree to stand down as long as Hezbollah was capable of firing rockets into Israel.

A draft resolution circulated Saturday by France among the 14 other Security Council members would call for an immediate halt to the fighting and establish a wide new buffer zone in south Lebanon monitored by international forces and the Lebanese army.

It remained unclear early Sunday who else Rice might see and where else in the region she might visit before completing her shuttle diplomacy and returning to the United States. Her weeklong trip has included last-minute schedule changes, including a surprise visit to Beirut last Monday.

All sides seemingly want the fighting to end, but the United States and Israel are pressing for a settlement that addresses enduring issues between Lebanon and Israel - not the quick cease-fire favored by many world leaders.

Hundreds of men, women and children have died, mostly Lebanese civilians killed in Israeli attacks. Less than four hours after Rice's arrival, a U.N. spokesman said two U.N. peacekeepers were wounded by an Israeli airstrike that hit their post in southern Lebanon. Last week, four peacekeepers died in an Israeli airstrike.

A top U.N. peacekeeping official predicted the war in southern Lebanon would continue until late August.

Hezbollah's leader, Sheik Hassan Nasrallah, did not appear impressed by Rice's efforts and said in a television address the Bush administration has no desire to end the fighting. He threatened more attacks deep into Israel.

"No matter how long the war lasts, whatever sacrifices it takes, we are ready. We will not be broken or defeated," he said.

The fighting broke out after Hezbollah launched a July 12 raid into Israeli territory. Two Israeli soldiers were captured. Israel says their release is pivotal to ending the current crisis.