BEIRUT, Lebanon — Israel launched a major attack deep into Lebanon, and Hezbollah said its guerrillas were fighting Israeli commandos trapped inside a hospital in the eastern city of Baalbek early today.

The Israeli army would not comment on the operation in the ancient city, which was once a Syrian army headquarters some 80 miles north of Israel. The Web site of the Israeli daily Ha’aretz reported that “helicopters put down Israel Defense Force commandos near Baalbek,” without adding details.

The ferocity of the battles in Baalbek and across southern Lebanon yesterday, the determination of the Israelis to keep fighting, and the minimal diplomatic progress toward a cease-fire all indicate the three-week-old war is more likely to escalate than end soon.

Hezbollah’s chief spokesman, Hussein Rahal, told the Associated Press that Israeli troops landed near Dar al-Hikma Hospital.

Four hours into the operation, fighting continued, witnesses said. By early this morning, Israeli warplanes had staged more than 10 bombing runs around the hospital as well as on hills in east and north Baalbek. The planes dropped flares over the city while heavy fighting raged around the hospital, they said.

“A group of Israeli commandos was brought to the hospital by a helicopter. They entered the hospital and are trapped inside as our fighters opened fire on them, and fierce fighting is still raging,” Mr. Rahal said.

He dismissed as “untrue” reports that the Israeli commandos managed to snatch some patients from the hospital and spirit them away in helicopters. Hezbollah’s capture of two Israeli soldiers in a July 12 cross-border raid triggered the Israeli offensive.

Witnesses said the hospital was hit in an Israeli air strike and was burning. Repeated telephone calls to the hospital went unanswered. Baalbek, about 10 miles from the Syrian border, is a city with spectacular Roman ruins as well as the barracks of the Iranian Revolutionary Guards when they trained Hezbollah guerrillas there in the 1980s.

The last time Israel forces were known to have gone that far on the ground into Lebanon was in 1994, when they abducted Lebanese guerrilla leader Mustafa Dirani, hoping to use him to get information about missing Israeli airman Ron Arad. Mr. Dirani was released in a prisoner exchange 10 years later.

In southern Lebanon yesterday, troops battled guerrillas after Israel ordered its army to punch all the way to the Litani River. Thousands of troops were operating along the Israel-Lebanon border. Additional soldiers crossed into Lebanon yesterday, Israeli defense officials said, joining forces already fighting there.

They entered through four different points along the border and moved at least four miles inside Lebanon. Thousands of reservists, called up over the weekend, also were gathering at staging areas on the Israeli side of the border, ready to join the battles and extend the invasion.

Israeli officials said their soldiers were to go as far as the Litani, about 18 miles from the border, and hold the ground until an international peacekeeping force comes ashore.

But the army later said it had distributed leaflets northeast of the river at villages where Hezbollah was active. The leaflets told people to leave, suggesting that the new offensive could take Israeli soldiers even deeper into Lebanon.

Despite mounting civilian deaths, President Bush held fast to support for Israel and was pressing for a U.N.resolution linking a cease-fire with a broader plan for peace in the Middle East. Staking out a different approach, European Union foreign ministers called for an “immediate cessation of hostilities” followed by efforts to agree on a sustainable cease-fire.

Prime Minister Olmert said it was not in Israel’s interest to agree to an immediate cease-fire because every day of fighting weakens the guerrillas.

“Every additional day is a day that drains the strength of this cruel enemy,” he said. “Every extra day is a day in which the [army] reduces their capability, contains their firing ability and their ability to hit in the future.”