Israeli army troops bombed Lebanon north of their self-declared buffer zone on Sunday after ordering people to leave seven more villages.
Air raids and artillery shelling were heard across southern Lebanon. Several people were reported killed and injured, with rescue teams searching for survivors.
The Israeli army said its targets were "terrorists and military infrastructure sites" used by Hezbollah, without providing evidence. Hezbollah meanwhile said it flew drones into an Israeli tank, and Israel said a soldier had been killed in combat.
The new attacks come despite Israel and Lebanon agreeing to extend a ceasefire by three weeks. The text of the agreement grants Israel the "right to take all necessary measures in self-defence".
Israel has also used the ceasefire to establish what it calls a "forward defence line" where its troops are operating inside Lebanese territory. More than a million people have been forced from their homes by Israeli displacement orders, largely in the south.
Army spokesman Lt Col Avichay Adraee on Sunday ordered people to leave seven villages in a patch of territory north of the line - Meidoun, Shoukin, Yahmar, Arnoun, Zawtar Al Sharqiya, Zawtar Al Gharbiyeh and Kfar Tebnit.
The order was followed by attacks in the area. An air strike at a roundabout in Kfar Tebnit killed several people, said Lebanon's National News Agency. It said a mosque and another religious building were destroyed in Zawtar Al Sharqiya.
Israel said the targets included Hezbollah cells preparing to carry out rocket attacks at Israel and its troops, a weapons storage site, and a member of the armed group riding a motorcycle. Prime Minister Benjamin Netanyahu said Israel would "act with a strong hand" in Lebanon despite the ceasefire.
"One might get the impression that the [Israeli army] is not active there. It is active, and it is acting with force," he said. "It must be understood that Hezbollah's violations are essentially disintegrating the ceasefire."
Hezbollah announced new drone attacks, including one at an Israeli artillery position in Al Bayyada. Responding to Mr Netanyahu, it said its attacks were a legitimate response to Israeli breaches of the ceasefire.
Lebanon was dragged into the regional war when Hezbollah, acting in solidarity with its key backer Iran, launched rocket fire at Israel last month.
The resulting Israeli offensive ended a tenuous 15-month ceasefire with Hezbollah. Israeli and Lebanese ambassadors have held two rounds of rare direct talks in Washington in a US-led push to resolve the latest conflict.
