Soon after the Cabinet decision, a column of Israeli tanks and armored vehicles crossed into southern Lebanon and took up positions inside Lebanese territory, witnesses said. The Litani River is about 18 miles north of the border.

Before the new offensive got off the ground, fighting intensified in the border strip that 10,000 Israeli troops were already occupying four miles into southern Lebanon.

Fifteen Israeli soldiers were killed in a single day of fighting Wednesday, the military said, the highest one-day total in the Israel-Hezbollah conflict. The military said 38 soldiers were wounded in battles across south Lebanon.

Israel also hit Lebanon's largest Palestinian refugee camp with an airstrike, killing at least two people. Israeli attacks Wednesday killed eight Lebanese civilians, according to Lebanese officials, and three guerrillas, according to Hezbollah.

An Israeli TV station, quoting unidentified sources, said Iranian Revolutionary Guard soldiers were among the Hezbollah dead. The Israeli military was unable to confirm the report. Israel has charged that Iran is aiding Hezbollah on the ground as well as supplying the guerrillas with weapons. Iran has denied the charges.

Israeli warplanes also dropped leaflets over the southern port city of Tyre and over Beirut proper for the first time. The fliers criticized Nasrallah, saying he was "playing with fire" and that the Lebanese people were "paying the price."

Hezbollah fired at least 170 rockets into Israel on Wednesday, the army said.

Since the fighting began, at least 711 people have died on the Lebanese side of the conflict. The Israeli death toll stood at 118, including 36 civilians and 82 soldiers.

Israel's Security Cabinet was told a new offensive could mean 100 to 200 more military deaths, according to a participant. Military officials said it would take the army several days to reach the Litani and then several more weeks to rid that area of Hezbollah's fighters and rocket launchers.

"The assessment is (the new offensive) will last 30 days," said Trade Minister Eli Yishai, a member of the Security Cabinet who abstained from the vote. "I think it will take a lot longer."

The offensive was expected to eliminate 70-80 percent of Hezbollah's short-range rocket launchers, senior military officials said.

The offensive was approved 9-0, with three abstentions at an intense six hour meeting. During the meeting, Secretary of State Condoleezza Rice called Prime Minister Ehud Olmert, and they spoke for half an hour, Israeli officials said. Upon his return to the room, Olmert told the ministers the offensive would be accompanied by a diplomatic initiative.

The government's decision came two days after Lebanon offered to send 15,000 soldiers to patrol the border region, a key Israeli demand intended to prevent attacks on Israel. The current fighting began when Hezbollah fighters crossed into Israel on July 12, killing three soldiers and capturing two others.

In a major shift, Nasrallah said Hezbollah supported a deployment by the Lebanese army after a cease-fire is declared and Israel leaves.

Israeli officials remained skeptical of the Lebanese offer and were not convinced Lebanon's army would take concrete action to stop Hezbollah attacks.

"It is important that the Lebanese army will be accompanied by an international force that will enable it to reach the south in an organized manner, and to leave the place clean of Hezbollah," Israeli Foreign Minister Tzipi Livni said.

Some soldiers said Israel was having trouble controlling even the small strip it was already occupying.

"The biggest problem is still the existence of Hezbollah fighters all over the place, even though we have most of the territory under control," said Maj. Avi Ortal, an officer in a reserve brigade in southwestern Lebanon.

"Hezbollah are good fighters. They know the territory. They live there and they have had six years to build compounds," he said.