Two Israeli soldiers have been killed in fierce fighting near the village and at least 17 others have been injured, Aljazeera television reported on Monday.
An Israeli Apache attack helicopter has also crashed 4km inside Israel causing unknown casualties. Hezbollah claimed to have shot it down but this was not confirmed by Israel.
Almost constant gunfire and explosions could be heard in southern Lebanon from the Israeli side of the border, and large plumes of grey smoke rose over the area.
Bint Jbail, a major town, is about 2km north of the hilltop village of Maroun al-Ras which was captured by Israel on Sunday after three days of heavy fighting.
The army said on Monday that it was expanding its ground operation in Lebanon, which had been limited during the two-week offensive, to pinpoint operations near the border.
Brigadier General Alon Friedman told Israel Army Radio that: "The scope continues to grow in recent days … We are advancing."
He said the operation would continue for up to 10 days "in order to achieve the basic goals we set down," including trying to stop Hezbollah rocket fire.
Hezbollah says that it has destroyed five Israeli tanks in the area surrounding Maroun Al-Ras since fighting began, Aljazeera television reported.
The conflict began after two Israeli soldiers were captured and eight killed by Hezbollah fighters in a cross-border raid on July 12.
The Israeli ground advance into southern Lebanon comes as Condoleezza Rice, the US secretary of state, arrived in Beirut to meet Fuad Siniora, the Lebanese prime minister.
The visit is an "important show of support for the Lebanese public and the Siniora government," a US official said on Monday.
Rice met Lebanon's prime minister Fouad Siniora in April
"The fact we are going to go right into Beirut after all that has happened is a pretty dramatic signal to Lebanon and their government," the official told reporters travelling with Rice.
Rice, who is also due to visit Israel, is expected to make an announcement on aid to Lebanon and also wanted to discuss with Lebanese leaders "the elements of the solution we can see now," the official said, without elaborating.
En route to the region, Rice had called for an "urgent ceasefire" in a conflict that has killed more than 360 people in Lebanon, mostly civilians, as well as 37 Israelis.
As well as Siniora, Rice will also meet Fawzi Sallukh, the foreign minister who is also close to Hezbollah, Nabih Berri the parliamentary speaker and other lawmakers including prominent Druze leader Walid Jumblatt.
Israeli air strikes
Israel has continued to bomb suspected Hezbollah individuals and positions and to hit Lebanese infrastructure.
The Israeli military has also said that it would destory 10 buildings in south Beirut, a pro-Hezbollah area, for every rocket fired at the Israeli port of Haifa, army radio said Monday.
"Army chief of staff Dan Halutz has given the order to the air force to destroy 10 multi-storey buildings in the Dahaya district (of Beirut) in response to every rocket fired on Haifa," a senior air force officer told the station.
Israeli helicopters also have fired at least five missiles into the Palestinian al-Rashidiya refugee camp in southern Lebanon on Monday morning.
The attack killed one person and injured six, Aljazeera television's correspondent in Lebanon reported.
"The scope continues to grow in recent days … We are advancing"
Alon Friedman, Israeli brigadier-general
Eleven others have reportedly been killed in more air strikes on the southern city of Tyre and Beirut's southern suburb.
Israel also killed one Lebanese civilian and wounded 10 others in a new wave of air strikes on the village of Hallusiya, north of the port city of Tyre, when a missile struck a house.
Further south, four residents of the village of Hinniya were wounded by missile shrapnel.
Six civilians were also wounded by air raids on the village of Dwair, near the main southern city of Sidon.
New rocket attacks
The Israeli military also said that Hizbollah fighters had also fired more rockets at northern Israel on Monday.
Rescue officials said two more rockets landed in the northern town of Kiryat Shmona.
No casualties or damage were reported.
According to Israeli officials the toll in Israel stands at 37, with 17 people killed by Hezbollah rockets and 20 soldiers killed in the fighting.
Sixty-eight soldiers have been wounded, and 255 civilians injured by rocket fire.