Israeli forces are carrying out "offensive action" across southern Lebanon, Defense Minister Yoav Gallant said Wednesday without specifying whether ground troops had crossed the border.

"Many forces are deployed on the border and IDF (army) forces are carrying out offensive action currently throughout southern Lebanon," Gallant said in a statement, also claiming that "half of Hezbollah's commanders in southern Lebanon have been eliminated" in months of violence.

"The other half are in hiding and abandoning the field to IDF operations," he added without giving a specific number.

In a separate statement, the army said it had struck 40 Hezbollah targets in southern Lebanon.

"A short while ago, IDF (army) fighter jets and artillery struck approximately 40 Hezbollah terror targets" around Aita al-Shaab in southern Lebanon, including storage facilities and weaponry, it said.

The army said Hezbollah "has established dozens of terror means and infrastructures in the area" to attack Israel.

Lebanon's state-run National News Agency said Israel had carried out more than 13 strikes near Aita al-Shaab and surrounding villages.

"Israeli warplanes carried out ... more than 13 air strikes targeting the outskirts of the towns of Aita al-Shaab, Ramya, Jabal Balat and Khallet Warda," it said.

The strikes came after Hezbollah said it fired a fresh barrage of rockets across the border on Wednesday after a strike blamed on Israel killed two civilians.

The group had already fired rockets at northern Israel late on Tuesday "in response" to the civilian deaths.

Cross-border exchanges of fire have flared between the Israeli army and Iran-backed Hezbollah since Hamas's 7 October attack on Israel triggered war in Gaza.

Since 7 October, at least 380 people have been killed in Lebanon, mostly Hezbollah fighters but also 72 civilians, according to an AFP tally.

Israel says 11 soldiers and eight civilians have been killed on its side of the border.