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A woman and her three grandchildren were killed on Sunday by an Israeli strike on their vehicle as they were driving near the town of Ainata in southern Lebanon.
They are the latest civilian casualties in cross-border fire between the enemy states that is threatening to become full-scale conflict.
Two other civilians were injured, one of whom was identified as journalist Samir Ayoub, a relative of the family. He was driving ahead of them in a separate car.
“The three little girls were burned in their car in front of my eyes and their mother was screaming,” he told Al Mayadeen news agency.
“I pulled her out of the car. Her children were burning and screaming in the car and I couldn’t do anything.”
The family was driving from the town of Aitaroun to Ainata when the second vehicle carrying the grandmother, the mother and her children was struck, Hezbollah said.
“The Islamic Resistance affirms that it will never tolerate harm and assault on civilians,” the Iran-backed group said. “Its response will be firm and strong.”
Hezbollah retaliated with a barrage of Katyusha rockets on the town of Kiryat Shmona.
The attack did not cause casualties, rescue services told Israeli newspaper Haaretz.
Earlier on Sunday, an Israeli army spokesman said one civilian near its northern border had been killed by an anti-tank guided missile launched from Lebanon.
Hezbollah claimed in a statement that the same attack had caused military casualties.
"Hezbollah continues to undermine security in the north, and targets residents in the north indiscriminately, while risking stability in southern Lebanon," Avichay Adraee, the Arabic-language spokesman for the army, told Israeli media.
Three paramedics were also injured on Sunday when an ambulance was hit by an Israeli strike in the southern Lebanese town of Tayr Harfa.
The day marked by the civilian deaths came nearly one month after the border conflict first erupted between Israel and armed groups led by Hezbollah.
“For every civilian, a civilian,” he promised in his televised speech.
The Lebanon-Israel front has largely been contained to the border, albeit gradually rising in intensity. Both sides have walked a fine line, favouring retaliatory strikes over full-scale assaults.
Funerals held for Hezbollah fighters in south Lebanon - in pictures
Mr Nasrallah reinforced concerns that a miscalculation or sudden violence could start a broader regional conflict, pitting Israel against Iranian proxies.
But he also made it clear that the group would react to escalations in Lebanon and Gaza.
“I tell the Israelis, if you are considering carrying out a pre-emptive attack against Lebanon, it will be the most foolish mistake you make in your entire existence,” Mr Nasrallah said.
“Whoever wants to prevent a regional war must hasten to stop this aggression.”
At least nine civilians have been killed in Israeli strikes on south Lebanon, including a Reuters journalist.
At least 60 Hezbollah fighters have been killed since the beginning of the border conflict on October 8. Israel has yet to release a tally of casualties on its side of the border.