Later, Hezbollah said it fired rockets at northern Israel in response.
Israel's military said it had targeted an arms depot and a military installation belonging to the powerful Iran-backed group.
"The Israeli enemy committed a massacre of civilians in the town of Bint Jbeil, with one brother and a sister in the Dagher family killed," the NNA reported.
It said another sister was gravely wounded when Israeli aircraft hit the family's house twice, destroying it.
Hezbollah in a statement later on Monday announced the death of one of its fighters from the Dagher family in Bint Jbeil, confirming the NNA's report.
An Israeli military statement said that aircraft "struck a Hezbollah weapons storage facility in the area of Bint Jbeil and a Hezbollah military structure... in southern Lebanon" near the border village of Kfar Kila.
The NNA also reported an Israeli strike hitting Kfar Kila.
On Monday night, Hezbollah said it fired dozens of rockets at an Israeli border town of Kiryat Shmona "in response to the aggression of the Israeli enemy including the horrible massacre in Bint Jbeil".
The Israeli military said it shot down about half of the roughly two dozen rockets fired, without mentioning any injuries.
Hezbollah has traded almost daily fire with Israeli forces in support of ally Hamas since the Palestinian militant group's October 7 attack on Israel triggered war in the Gaza Strip.
The violence, largely restricted to the border area, has raised fears of all-out conflict between the foes, who last went to war in the summer of 2006.
In Lebanon, the cross-border violence since October has killed 505 people, mostly fighters but also including 98 civilians, according to an AFP tally.
On the Israeli side, at least 29 people have been killed, the majority of them soldiers, according to the authorities.
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