An Israeli official said early on Tuesday that the military had recommended an expansion of the offensive, which could take Israeli soldiers several kilometers deeper into Lebanon.
"The security cabinet approved a widening of ground operations without any objections," the Israeli government official said.
The Israeli army has so far stayed within 2-3 kms of the border although air strikes have been carried out across the country.
Israel's radio also announced on Tuesday morning that an additional 15,000 reservists would be called up.
Israeli leaders have said they want to create a "security zone" about 1.5 km wide that would be free of active Hezbollah members.
The Israeli cabinet's decision means that the army can now choose when or whether troops should push deeper into Lebanon.
"The security cabinet approved a widening of ground operations without any objections"
An Israeli government official
An Israeli official, speaking on condition of anonymity because he was not authorised to talk to reporters, said there was no deadline for the Israeli offensive to end.
The United Nations Security Council is expected to debate a resolution this week about a cease-fire.
Israeli forces have been trying to drive Hezbollah back from the border and end rocket attacks on Israeli cities since the Lebanese group abducted two soldiers in a cross-border raid on July 12.
The limited Israeli ground forces that have entered south Lebanon so far have faced tough opposition from Hezbollah fighters there.
Israel has been wary of getting bogged down in territory from which it withdrew in 2000 after 22 years of occupation.
Last week, Israel called up at least 15,000 reserve soldiers to allow for a possible expansion of the offensive.