Hezbollah on Monday claimed attacks on troops and military positions in northern Israel, including a drone strike on a base and an assault on soldiers allegedly "infiltrating" near the Lebanese border.

The Iran-backed group has exchanged regular cross-border fire with the Israeli army in support of ally Hamas since the Palestinian militant group's October 7 attack on Israel sparked the Gaza war.

Fears of a major escalation skyrocketed after an Israeli strike last month on Beirut's southern suburbs killed Fuad Shukr, one of Hezbollah's top commanders, hours before an attack in Tehran, blamed on Israel, killed Hamas's political leader Ismail Haniyeh.

Iran and Hezbollah have vowed to respond.

Hezbollah said Monday it launched a "simultaneous air attack" with "explosive-laden drones" on two Israeli military positions -- a barracks near the border and a base near the coastal town of Acre, around 15 kilometres (10 miles) from the frontier.

It said it came "in response" to an Israeli "attack and assassination" in south Lebanon's Tyre area.

A fighter from the group was killed in an Israeli strike in the area on Saturday.

The Israeli military had said its aircraft "eliminated" a Hezbollah operative in the Tyre area, describing him as a "commander" in the group's elite Radwan force.

Overnight, Hezbollah said its fighters targeted a group of Israeli soldiers "infiltrating" near the border and confronted them "with rocket weapons and artillery, forcing them to return".

Also Monday morning, Hezbollah claimed a rocket and artillery attack on another Israeli barracks in stated retaliation for "Israeli enemy attacks".

The cross-border violence has killed some 582 people in Lebanon, mostly Hezbollah fighters but including at least 128 civilians, according to an AFP tally.

On the Israeli side, including in the annexed Golan Heights, 22 soldiers and 26 civilians have been killed, according to army figures.