MARJAYOUN, Lebanon – Cars and trucks packed with women and children, mattresses strapped to the roofs and white flags streaming from the windows, made their way to the coast. They then turned north, passing flattened houses, shattered trees and burned-out cars strewn on the roadside. At one point north of Tyre, vehicles gingerly made their way around a gigantic crater half filled with water into which a car had toppled when a missile struck.

Hundreds of people fled southern Lebanon on Monday, taking advantage of a lull in Israeli bombardment. The guerrillas also paused their rocket attacks into northern Israel.

In the Israeli town of Nahariya, residents who had been hiding in shelters began emerging. Supermarkets were fuller than before and more people were in the streets.

But both sides knew major fighting would resume soon. Diplomatic efforts to end the crisis faltered, despite increased world pressure for a cease-fire after the devastating strike in Qana.

Israeli warplanes hit Hezbollah fighters battling with soldiers near the border as the guerrillas fired mortars into Israel.

Israel’s prime minister declared there would be no cease-fire with Hezbollah, apologizing for the deaths of Lebanese civilians but saying “we will not give up on our goal to live a life free of terror.” 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.