SIDON, Lebanon (AP) – 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 Rice’s 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 Lebanon’s 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 in remarks published Monday 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.

An Israeli helicopter crashed in northern Israel after hitting an electrical wire while making an emergency landing, killing both pilots.

Hezbollah said it caused Israeli casualties in hits on five tanks on the road to Bint Jbail and around Maroun al-Ras, a hilltop village closer to the border that Israeli ground forces seized in heavy weekend fighting.

Israel said its troops captured two Hezbollah guerrillas, the first it had taken in the Lebanon fighting. Brig. Gen. Alon Friedman said they are being held in Israel “with the aim of interrogating them.”

Hezbollah continued its missile attacks on northern Israel, firing more than 80 rockets and slightly wounding 13. Militants fired 95 rockets on Sunday and 129 on Saturday, the Israeli military said. U.N. observers in south Lebanon said the Israeli numbers appear accurate.

Sunday was one of the heaviest days of Israeli bombardment, with 270 targets, compared with 120 the day before, according to the military.

At least 384 people have been killed in Lebanon, including 20 soldiers and 11 Hezbollah fighters, according to security officials. At least 600,000 Lebanese have fled their homes, according to the WHO _ with an estimate by Lebanon’s finance minister putting the number at 750,000, nearly 20 percent of the population.

Israel’s death toll stands at 39, with 17 people killed by Hezbollah rockets and 22 soldiers killed in the fighting.

Up to 40 percent of the 200,000 Lebanese who live in villages along territory closest to the border are likely still in their homes, unable or too afraid to move because of Israeli shelling, U.N. observers said.

More foreigners fled Lebanon by sea from Beirut. A Greek ferry commissioned by European countries arrived in Tyre and took on hundreds of stranded foreigners.

A group of 300 Americans and 100 other Europeans were believed trapped in villages south of Tyre, said Erik Rattat, a German official involved in the operation. It did not appear that they made it to the ship. An Associated Press reporter at the scene an hour before it left said they had not arrived, and the U.S. Embassy could not immediately say if they had reached the ship in time.

Some 11,700 Americans have fled Lebanon, the State Department said. U.S. Consul William Gill said most Americans who wanted to leave had done so by Sunday.

President Bush ordered a fleet of U.S. helicopters and ships to carry badly needed humanitarian supplies into Lebanon.

“I am deeply concerned about the Lebanese people and what they are enduring,” Rice said before meeting Berri. “I am obviously concerned about the humanitarian situation.”

Officials have been trying to move aid along shattered roads to the south where it’s needed most _ although Israel has not defined a safe route to the region.

Two convoys carrying generators for hospitals, food, tarpaulins and hygiene kits were heading from Beirut to Tyre and the southern city of Marjayoun, said Hisham Hassan, ICRC spokesman in Lebanon.

Aid was starting to move into Beirut’s port after Israel opened it for humanitarian ships. An Italian warship brought food, medicine, tents, blankets, water, electrical generators and ambulances. A ferry carrying supplies from France also arrived.

U.N. humanitarian chief Jan Egeland appealed for $150 million in humanitarian aid for the next three months for food, health care, water and sanitation. He said 500,000-800,000 people have been affected by the fighting.

Egeland said he was asking the Israelis for safe passage for aid ships to enter the northern port of Tripoli and the southern port of Tyre. So far, Israel has loosened its sea blockade only for Beirut.

Rice’s unannounced visit aimed to show support for the embattled, Western-backed government and to tackle what the United States and Israel believe to be the key to bringing peace: ending Hezbollah’s domination along the Israeli border.

Her mission is the first U.S. effort on the ground to try to resolve the crisis that began July 12 with Israel’s onslaught on Lebanon sparked by Hezbollah’s capture of the two Israeli soldiers. Rice flew by helicopter from Cyprus to Beirut, then traveled under heavy guard in a motorcade to Saniora’s office.

She praised Saniora’s “courage and steadfastness.” After meeting for more than an hour, they left without speaking to reporters.

She was in the city for about five hours and then returned to Cyprus.

The White House has said an international force may be needed to help the Lebanese army move into the south, which the Beirut government has long refused, wary of confronting the guerrillas’ power there and of tearing apart the country.

Arab heavyweights Egypt and Saudi Arabia were pushing Syria to end its support for the guerrillas, Arab diplomats in Cairo said. Israel signaled a policy shift, saying it would accept an international force _ preferably from NATO _ to ensure the peace in southern Lebanon.

British Prime Minister Tony Blair said he hoped to give details of a cease-fire plan in the next few days.

In Tehran, a Hezbollah representative in Iran warned that his militant group plans to widen its attacks on Israelis until “there will be no place they are safe.” Hossein Safiadeen said there would be “a new Middle East in the way of Hezbollah and Islam, not in the way of Rice and Israel.”

En route, Rice discussed possibly working with Syria on a solution. The Bush administration has blamed Syria _ and Iran _ for stoking the violence by encouraging Hezbollah to attack northern Israel.

“The problem isn’t that people haven’t talked to the Syrians. It’s that the Syrians haven’t acted,” she said. “It’s not as if we don’t have diplomatic relations. We do.”

Rice has tried to walk delicately between supporting the Lebanese government while also not dictating to its ally Israel how it should handle its own security. Her posture has frustrated numerous allies.

“We all want to urgently end the fighting. We have absolutely the same goal,” Rice said.