The announcement by Mr. Netanyahu prompted thousands of residents to flee their homes, clogging the roads out of the area late Monday morning. For many residents, the sudden exodus has become a miserable routine over nearly three years of conflicts between Hezbollah and Israel.

“I lost count of how many times I’ve evacuated,” said Zahra Khomasi, 43, as she sat in her car in Tayouneh on the outskirts of Dahiya.