In addition, a top Israeli officer, Major-General Udi Adam, said the offensive would continue for "several more weeks".
Israeli Justice Minister Haim Ramon told army radio: "Yesterday in Rome we have in effect obtained the authorisation to continue our operations until Hezbollah is no longer present in southern Lebanon."
"The whole world knows that a Hezbollah victory will mean a victory for international terrorism, which will be a catastrophe for the world and for Israel," he said.
Mr Ramon was speaking ahead of an Israeli cabinet meeting that is due to decide whether to expand the offensive, now in its 16th day.
In other recent developments:
Israeli warplanes have carried out new air strikes on south Lebanon and the Bekaa Valley to the east of the capital, keeping up the pressure on two strongholds of the militant group Hezbollah.
In air raids to the east of Sidon, the regional capital of the south, one person was seriously wounded in the village of Zefta, police said. A home was destroyed in Bazalieh to the north of Baalbek in the Bekaa.
A security official told the news agency ANI that Israeli warplanes fired more than 400 missiles overnight at Khiam in the south.
Security sources said Israeli warplanes destroyed radio communication masts north of Beirut and attacked three trucks carrying medical and food supplies to the east, killing two truck drivers.
A Lebanese military source told AFP that Israeli warplanes carried out a raid near a Lebanese army base in the Amchit region 40 kilometres north of Beirut without causing any casualties.
Israeli aircraft blasted targets in and around several villages and towns in the mainly Shi'ite Muslim south, and artillery batteries opened up from Israel's side of the border.
Hezbollah guerrillas, who have kept up rocket attacks on northern Israel, killed nine Israeli soldiers in house-to-house fighting in a border town and a nearby village.
In developments in the Gaza Strip:
According to Palestinian reports, a 75-year-old Palestinian woman was killed and her two sons were injured after an Israeli grenade hit the woman’s house.
Palestinian legislator Saeb Erekat has complained that the Lebanon conflict has distracted attention from the Gaza fighting.
Khader Habib, a leader of Islamic Jihad in Gaza, said his group would respond to the latest deaths with rocket attacks and suicide bombings against Israeli soldiers.
