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A couple and their son were killed in an Israeli air strike on their home in the village of Hula in southern Lebanon.
Hassan Kassem, his wife Roueida Moustapha and their son, Ali, 25, died in the attack, Lebanese media reported.
Israel military and Iran-backed Hezbollah militants have exchanged near-daily fire across the border since October 8 because of the war in Gaza, amid concerns of an all-out conflict.
About 30 rockets were fired from Lebanon in the latest barrage on Kiryat Shmona, according to the Israeli military.
It also said that at least 10 were successfully intercepted by the Iron Dome.
On Tuesday, Hezbollah claimed several attacks on Israeli military positions.
The group said in a statement that it killed and wounded Israeli soldiers inside a Merkava tank in northern Israel and accused Israel of bombing Lebanese villages and civilians.
On Monday, three paramedics affiliated with Hezbollah were killed in an Israeli strike in the village of Adaisseh, in southern Lebanon.
Hezbollah deputy Ali Fayyad said on Tuesday the attack "will not go unpunished", the National News Agency reported.
Human Rights Watch said the recent rise in civilian casualties in southern Lebanon was "extremely worrying".
Cross-border hostilities have been escalating in recent weeks, despite US-led diplomatic effort to avert a full-scale war between Israel and Hezbollah
At least 302 people have been killed in Lebanon. Most of the casualties were Hezbollah members, but 52 were civilians, AFP reported.
In Israel, at least 10 soldiers and seven civilians have been killed.