Israeli Prime Minister Ehud Olmert says the attacks on Lebanon will be kept up until two captured soldiers are freed.
Civilian casualties are mounting on both sides of the border
He also insisted Hezbollah guerrillas had to be disarmed and the Lebanese army had to control southern Lebanon.
"We are not looking for war or direct conflict, but if necessary we will not be frightened by it," he said.
More than 200 Lebanese people have died in six days of Israeli bombardment. Hezbollah has fired hundreds of rockets into Israel, killing about 12 people.
A fresh barrage of rockets was fired at Israel on Monday evening, officials said. One landed close to a hospital in the northern town of Safed, injuring at least six people, medics quoted by Reuters news agency said.
There were also reports of renewed Israeli air strikes on Hezbollah strongholds in Lebanon overnight.
In Israeli strikes on Monday, at least 10 Lebanese people died when their vehicles were hit on a bridge in the south of the country, reports said.
At least 17 people died elsewhere, as Israeli air strikes targeted the northern city of Tripoli, the nearby port of Abdeh and the capital, Beirut.
The bodies of nine people, including six children, were reportedly found in the rubble of a building in Tyre hit by Israeli missiles on Sunday. One report said they had been trying to shelter in the basement.
Israeli ground forces also entered southern Lebanon, but Israeli officials said it was not the start of a large-scale invasion.
Israel launched its offensive last Wednesday following the capture of the two soldiers in a cross-border raid by Hezbollah.
At least four people were hurt in a fresh attack on Haifa
As the Israeli attacks continue, large numbers of people in the south have abandoned their homes.
A BBC correspondent travelling through the south says the roads are clogged with packed vehicles. Many of the displaced, he says, appear exhausted and bewildered.
A number of countries are planning major sea evacuations of their nationals from Lebanon.
The European Union has appealed for an end to hostilities. The UN Security Council has again met to discuss the crisis, although a BBC correspondent says it will not take any action until a team of UN envoys returns from the region later in the week.
UN chief Kofi Annan and UK PM Tony Blair have called for an international force to be sent to Lebanon.
The force could "stop the bombardment coming over into Israel and therefore gives Israel a reason to stop its attacks on Hezbollah", Mr Blair said.
Mr Annan suggested a "package of actions, not exhortations" that would require parties to release prisoners, stop both rocket attacks into Israel and retaliatory action and "pursue this idea of a stabilisation force".
Israeli spokeswoman Miri Eisin told the BBC it was too early to consider a new force.
In other developments:
- Lebanese TV showed footage of what it said was an Israeli F-16 fighter aircraft falling from the sky over Beirut in flames, but Israel said none of its aircraft had been shot down, and said it was a missile
- An Italian ship took some 366 Europeans out of Beirut to Cyprus, while a cruise ship chartered by France is due to arrive in Larnaca with hundreds more
- French Prime Minister Dominique de Villepin arrived in Beirut as an expression of solidarity with the Lebanese people
- The US said Secretary of State Condoleezza Rice would be travelling to the region, although a date was not set
- UN special envoy Vijay Nambiar spoke of "promising" first steps after ceasefire talks in Beirut, but said much work remained to be done; he meets Israeli Foreign Minister Tzipi Livni on Tuesday
Israeli forces have also kept up their offensive in the Gaza Strip - which began after an Israeli soldier was seized by Palestinian militants last month.