Two Israeli soldiers have been killed in fierce fighting near the border and at least 17 others have been injured, Aljazeera television reported on Monday.
An Israeli Apache attack helicopter also crashed 4km inside Israel killing two airmen. Hezbollah claimed to have shot it down but an Israeli army spokeswoman said it may have been due to a technical fault.
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.
Israel plans a sweep of Bint Jbeil, which army spokeswoman Brigadier-General Miri Regev said had become a "centre for Hezbollah terrorists" firing Katyusha rockets across the border.
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.
Israel has continued to bomb suspected Hezbollah individuals and positions and to hit Lebanese infrastructure.
At least seven civilians, including two children, were killed and at least 50 wounded in air strikes on southern Lebanon. Bombs also hit a Shia area of Beirut.
The Israeli military has said it will destroy 10 buildings in predominantly Shia south Beirut for every rocket fired at the Israeli port of Haifa, army radio said Monday.
More Hezbollah rockets have hit
towns in northern Israel
The Israeli army said at least 20 Hezbollah rockets struck Haifa, Nahariya and the border town of Shlomi, wounding at least four people. Rockets have killed 17 Israeli civilians since the conflict began. Twenty soldiers have also died.
Hezbollah leader Hassan Nasrallah remained defiant, saying that deeper incursions would not stop the rocket attacks, and ruling out a negotiated settlement unless it involved a prisoner swap.
"We are truly in a state of war and Hezbollah's priority is to stop the savage Zionist aggression on Lebanon," he told As-Safir newspaper. "We do not feel that we are currently interested in discussing ideas or initiatives."
The Israeli military has also said that it would destroy 10 buildings in south Beirut, a pro-Hezbollah area, for every rocket fired at the Israeli port of Haifa, army radio said Monday.
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 United Nations has launched an appeal for $150 million in aid for the people of Lebanon.
Jan Egeland, the UN emergency relief coordinator said this was "the hour of greatest need for the Lebanese people."
The money would cover the needs of 800,000 people for three months, including food, health care, water and sanitation.
Aid efforts have been hindered by Israel's destruction of civilian infrastructure including roads and bridges and its targeting of commercial trucks, a UN statement said.
"The ongoing hostilities continue to prevent access to affected populations and free movement of relief staff and goods," the statement said.