SIDON, Lebanon – Israeli ground forces pushed deeper into Lebanon on Monday in fierce fighting and captured two Hezbollah guerrillas, while two aid convoys carrying food, generators and other badly needed supplies left Beirut for two southern cities.

Four Israeli soldiers were killed – two in fighting and two in a helicopter crash – and 20 were wounded, military officials said.

Secretary of State Condoleezza Rice made a surprise visit to Beirut to launch diplomatic efforts aimed at ending 13 days of warfare. Prime Minister Fuad Saniora told her his government is hoping to “put an end to the war being inflicted on Lebanon.” He told Rice that Israel’s bombardment was taking his country “backward 50 years.”

An official close to parliament speaker Nabih Berri, a close Hezbollah ally, said his talks with Rice failed to “reach an agreement because Rice insisted on one full package to end the fighting.” The official spoke on condition of anonymity because the talks were private.

David Welch, an assistant secretary of state traveling with Rice, said later it was “unfair” to say the meeting with Berri went poorly.

Israel has not bombed Beirut since Sunday afternoon and appeared to have stopped all airstrikes on the city in deference to Rice’s visit. Rice later flew to Jerusalem.

Saniora has pleaded with Washington to press Israel to call a total cease-fire in bombardment that has demolished infrastructure and killed hundreds. President Bush has opposed an immediate cease-fire, saying the root cause of the conflict must be resolved.

Hezbollah leader Sheik Hassan Nasrallah said the priority is for a cease-fire and he was open to discussing ideas on ending the crisis.

Secretary-General Kofi Annan said he wants a meeting Wednesday in Rome on the Mideast violence to agree on a package including a cease-fire, deployment of an international force and the release of two Israeli soldiers abducted by Hezbollah.

Fierce fighting raged at the border as Israeli troops moved deeper into Lebanon to besiege the biggest town close to the frontier – Bint Jbail, nicknamed the “capital of the resistance” due to its intense support of Hezbollah during Israel’s 1982-2000 occupation of the south. Two Israeli soldiers were killed and 20 were wounded, the military said.

Bint Jbail holds strong symbolism for Hezbollah. Signs in the city tout its nickname, earned for its vehement backing of the guerrillas even while Israeli troops held the south. A day after Israel ended its occupation in 2000, Nasrallah went straight to Jbail for his first celebration rally.

Much of the town’s population of 30,000 is believed to have fled, but many remain. A Red Cross doctor who visited Sunday, Dr. Hassan Nasreddine, said he saw families crowded into schools, mosques and other shelters.

Following an intense artillery barrage, Israeli troops took control of a hilltop in Bint Jbail, but the rest of the town was held by Hezbollah guerrillas, military officials said.