Tens of thousands of people fled southern Lebanon as Israel vowed Tuesday to “accelerate” an aerial offensive that already inflicted the country’s deadliest day since war nearly two decades ago.

The Israeli military said it would be operating at “full force” as the death toll in Lebanon rose past 500 people and Hezbollah launched a new barrage of cross-border fire, an intensifying exchange between the U.S. ally and Iran-backed militant group that has stoked mounting fears of an…