The mayor who was killed was active in the nearby town of Sohmor.
At the same time, Israel's military has issued a warning to civilians in or near two buildings in the densely populated Beirut suburb of al-Dahiya.
In a post published on X, the military's spokesperson Avichay Adraee urges affected Lebanese to "urgently" evacuate. The area of al-Dahiya is known as one of Shia militia Hezbollah's strongest strongholds.
On Saturday, drones were fired from Lebanon towards Benjamin Netanyahu's residence. A few hours after the attack, the Israeli Prime Minister claimed that "nothing will deter us".
We will continue until we win, he said in a video recording, according to the newspaper Haaretz.
On Saturday, repeated rocket alarms have sounded in several places in northern Israel.
Two people are also reported to have been killed in an Israeli attack on a car in Jounieh north of Lebanon's capital Beirut.
