JERUSALEM – Israel’s prime minister declared Monday that there would be no cease-fire with Hezbollah guerrillas, apologizing for the deaths of Lebanese civilians but saying “we will not give up on our goal to live a life free of terror.” His Security Cabinet approved widening the ground offensive.

Israeli warplanes hit Hezbollah fighters battling with soldiers near the border as the guerrillas fired mortars into Israel. But an Israeli suspension of most airstrikes in Lebanon – and a pause by the guerrillas on rocket attacks in northern Israel – brought both countries their quietest day since the conflict began three weeks ago.

Lebanese fled north in overflowing trucks and cars. About 200 people – mostly elderly – escaped the border town of Bint Jbail, where Israeli troops and Hezbollah guerrillas fought their bloodiest clashes. Two residents dropped dead on the road out, one of malnutrition, the other of heart failure.

Some survivors described living on a piece of candy a day as the fighting raged.

“All the time I thought of death,” said Rimah Bazzi, an American visiting from Dearborn, Mich., who spent weeks hiding with her three children and mother in the house of a local doctor.

The lull was felt across northern Israel, too. In the town of Nahariya, residents who had been hiding in shelters for the better part of three weeks began emerging. Supermarkets were fuller than before and more people were in the streets, walking along the beach and shopping.

But diplomatic efforts to end the crisis faltered, despite increased world pressure for a cease-fire after the devastating strike in Qana.

Israel’s Security Cabinet early Tuesday approved widening the ground offensive, a participant said, and rejected a cease-fire until an international force is in place in southern Lebanon.

The participant, speaking on condition of anonymity because he was not authorized to talk to reporters, said Israel’s airstrikes would resume “in full force” after a 48-hour suspension expires in another day.

Israel called the 48-hour suspension after the Qana attack to give time for an investigation – though it said its warplanes would still hit urgent Hezbollah targets, and at least three strikes took place Monday.

Israeli Prime Minister Ehud Olmert apologized for the civilian deaths in Saturday’s strike, in which 56 people, mostly women and children, were killed.

“I am sorry from the bottom of my heart for all deaths of children or women in Qana,” he said. “We did not search them out … They were not our enemies and we did not look for them.”