Israel hopes to complete the new push in up to two weeks, Israeli Cabinet ministers said.
The decision was made late Monday by Israel's Security Cabinet. It followed a lull in fighting, imposed by the world's outrage over the killing of 56 Lebanese, most of them children, in an Israeli airstrike over the weekend in the town of Qana, the AP reports.
Following that deadly attack, Israel suspended most air strikes for 48 hours and Hezbollah drastically cut back rocket attacks Monday, after firing an average of more than 100 rockets a day in three weeks of fighting.
But by early Tuesday, Israel had resumed air raids. Warplanes targeted a Hezbollah stronghold deep inside Lebanon and Hezbollah fighters battling with soldiers near the Israel-Lebanon border. The Israeli army also reported heavy fighting between troops and Hezbollah in the south Lebanon village Ayt ash Shab.
Diplomatic efforts to end the crisis faltered, despite increased world pressure for a cease-fire after the devastating strike in Qana. Israeli Prime Minister Ehud Olmert said the offensive would continue until Hezbollah has been neutralized. "We will not give up on our goal to live a life free of terror," Olmert said.
U.S. President George W. Bush also resisted calls for an immediate halt to fighting, saying any peace deal must ensure that Hezbollah is crippled. He said Iran and Syria must stop backing the Shiite militant group with money and weapons.
Israel's Cabinet decision paved the way for a significantly broader ground offensive.
Up to now, several thousand soldiers had been engaged, fighting house-to-house battles with hundreds of Hezbollah fighters in Lebanese towns and villages close to the border. Last week, the Cabinet called up some 30,000 reserve soldiers, many of whom reported to their bases earlier this week to begin training.