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Lebanon's Hezbollah and Israel exchanged deadly border fire Sunday, with the Iran-backed group claiming responsibility for strikes that Israel said killed a civilian, further raising cross-border tensions amid Israel's Gaza onslaught.

The Israeli army closed the border area to civilians as tit-for-tat fire with Hezbollah and allied Palestinian factions in Lebanon intensified, killing more than 10 people in Lebanon and at least two in Israel since last Sunday.

"The IDF (Israel Defense Forces) responded with fire and destroyed Hezbollah positions and the source of the fire," an army spokesman said.

"In addition, there was fire at an Israeli military position. There were no casualties. The IDF responded with fire to the source of fire there too."

A military spokesperson told AFP that, "we have a dead civilian and a number of people wounded in the attack" by an anti-tank missile in Shtula.

"In accordance with the situational assessment and the recent shooting incident in northern Israel, the area up to four kilometres (2.5 miles) from the northern border with Lebanon has been closed," the army said in another statement.

Hezbollah on Sunday morning said it had "targeted a Zionist enemy army centre in the Shtula area with guided missiles."

In a separate statement, the group said one of its fighters had died Sunday. A spokesperson told AFP the fighter died after sustaining injuries in south Lebanon prior to Sunday, and that Israel was responsible.

Hezbollah said the strikes were retaliation for separate "Israeli aggressions" that killed two civilians and struck journalists, killing a Reuters videographer and wounding others -- including two from AFP.

Lebanon's army blamed an Israeli rocket which hit a car belonging to the journalists. Israel's army said it was "looking into" who launched the strike.

Two Lebanese civilians were killed in Israeli shelling of a southern village on Saturday, its mayor told AFP. Hezbollah said one of its fighters was also killed by Israeli fire.

Earlier Sunday Palestinian group Hamas claimed responsibility for two infiltrations from Lebanon to Israel that killed three of its fighters.

On Monday, Hezbollah said Israeli strikes had killed three of its members, after Palestinian fighters tried to infiltrate into Israel from Lebanon.