A Lebanese couple and their son were killed Tuesday in an Israeli strike on a house in the southern border village of Hula, the Lebanese official National News Agency reported.

Lebanon's Iran-backed Hezbollah movement and Israel have traded deadly cross-border fire on a near-daily basis since war broke out in October between Israel and Gaza's Hamas rulers, a Hezbollah ally.

"The three civilians, Hassan Hussein, his wife, Ruwaida Mustafa, and their 25-year-old son, Ali Hussein, were killed in the enemy raid on a three-storey house in Hula," NNA said.

"Search operations and the removal of rubble are continuing," it added.

Shortly after the deadly strike, Hezbollah said it launched "dozens of rockets" at the Israeli kibbutz of Kfar Blum, six kilometres (about four miles) from the nearest border point.

The Iran-backed group also said it "targeted a building" in the Israeli city of Kyriat Shmona.

It said it acted "in response to the Israeli aggression against the villages of the south and the homes of civilians," among them the strike on the house in Hula.

The Lebanese Shiite movement also said it carried out several attacks on Israeli military positions on the border on Tuesday.

On Monday, a missile fired from Lebanon killed a foreign worker in Israel, according to the army, and three Hezbollah-affiliated paramedics were killed in an Israeli raid on southern Lebanon, according to the group.

NNA had also reported on Monday evening that Israeli air raids targeted the border town of Bint Jbeil, but no casualties were reported.

It came as US envoy Amos Hochstein said a diplomatic solution was key to ending nearly five months of intensifying hostilities between Hezbollah and Israel.

"A diplomatic solution is the only way to end the current hostilities" and achieve "a lasting fair security arrangement between Lebanon and Israel", he said, adding "a temporary ceasefire is not enough".

Israeli Defence Minister Yoav Gallant has said there will be no let-up in Israeli action against Hezbollah even if a Gaza ceasefire is secured.

On Tuesday, the chief of Hezbollah's parliamentary bloc, Mohamed Raad, was quoted by NNA as saying: "We do not wish for war but we are ready to face it."

"We have not used all of our weapons, nor the weapons of open conflict. We have not deployed all of our arsenal, and the enemy knows it," he said.

The fighting has killed at least 302 people in Lebanon, most of them Hezbollah fighters but also including at least 51 civilians, according to an AFP tally.

In Israel, at least 10 soldiers and seven civilians have been killed.