Lebanon’s official National News Agency reported artillery shelling in the towns of Ayta al-Shaab and Bent Jbeil in southern Lebanon.
An airstrike also targeted a car in the town of Markaba, leaving two people injured, the state agency said.
Israeli tanks also fired shells on the town of Wazzani and at the outskirts of Kfarshouba in southern Lebanon.
Israeli reconnaissance planes also flew over the districts of Tyre and Bent Jbeil on Thursday morning.
The Israeli army warned Lebanese civilians early Thursday to stay clear of 10 villages in southern Lebanon until further notice, warning that anyone who “crosses the line puts himself in danger”.
The Lebanese army also said Thursday that it began assuming its missions in southern Lebanon.
A military statement announced that army units began to assume their missions in the south, the Bekaa region, and southern Beirut, including setting up checkpoints, opening roads, and detonation of unexploded ordnance.
“These missions are part of the army’s ongoing efforts to keep pace with the movement of displaced people, help them return to their villages and towns, and maintain their security and safety,” it added.
The army noted these missions come as the deployment of its forces is being boosted south of the Litani River.
The cease-fire deal took effect early Wednesday to end more than 14 months of fighting between the Israeli army and Hezbollah.
Under the terms of the cease-fire, Israel will withdraw its forces south of the blue line de facto border in a phased manner while the Lebanese army deploys its forces in southern Lebanon within a period that does not exceed 60 days.
Implementation of the agreement will be overseen by the US and France, but details on enforcement mechanisms remain unclear.
More than 3,800 people have been killed in Israeli attacks in Lebanon and over 1 million displaced since October last year, according to Lebanese health authorities.