An Israeli strike Tuesday killed a local Hezbollah commander in south Lebanon, the Israeli army said, with the Iran-backed group saying three of its members were killed and launching rockets in retaliation.

Israel and Hamas ally Hezbollah have been exchanging near-daily cross-border fire since the Palestinian militant group attacked southern Israel on 7 October, triggering war in the Gaza Strip.

Tuesday's exchanges came with regional tensions high after Iran launched missile and drone attacks on Israel over the weekend in retaliation for a deadly Israeli strike on Tehran's consulate in Damascus.

The Israeli military said its "aircraft struck and eliminated Ismail Yusef Baz, the commander of Hezbollah's coastal sector", adding he was killed in south Lebanon's Ain Baal area.

Aircraft also hit "Hezbollah military structures and terrorist operatives" elsewhere in south Lebanon on Tuesday, it said in a separate statement.

Lebanon's official National News Agency (NNA) reported one dead in an Israeli strike on a car in Ain Baal, about 15 kilometers (nine miles) from the border.

Hezbollah said in a statement that Baz had been killed, without mentioning his rank or role, while a source close to the group told AFP that "the field commander in charge of the Naqura region" had been killed "in an Israeli strike".

The NNA also said an "enemy strike" targeted two cars in Shehabiya, about 10 kilometers from Ain Baal, reporting an unspecified number of dead and wounded.

Hezbollah later said that two more of its fighters had been killed, while its ally the Amal movement announced one dead in Ain Baal.

Hezbollah said it launched rockets at several Israeli military bases "in response to the Israeli enemy's attacks" on Lebanese villages, in particular Ain Baal and Shehabiya.

Earlier Tuesday, Hezbollah had said its fighters launched an "air attack with suicide drones in two phases... striking the Iron Dome (air defense system) platforms and their crew" in the Beit Hillel area. 

The Israeli military said "two armed" drones entered from Lebanon and exploded near Beit Hillel, with local Israeli authorities saying three people were wounded.

On Monday, Hezbollah targeted Israeli troops with explosive devices, wounding four soldiers who crossed into Lebanese territory, the first such attack in six months of clashes.

The violence has killed at least 368 people in Lebanon, mostly Hezbollah fighters but also including at least 70 civilians, according to an AFP tally.

In Israel, the military says 10 soldiers and eight civilians have been killed since hostilities began.

Tens of thousands of civilians have fled their homes on both sides of the border, with the violence fuelling fears of all-out conflict between Hezbollah and Israel, which last went to war in 2006.