An Israeli air attack in south Lebanon has killed four civilians – three children and their grandmother – raising the likelihood of a dangerous new escalation in the conflict on the Lebanon-Israel border.

Israeli troops and Lebanon’s Hezbollah fighters and their allies have been clashing for a month along the border since the start of the Israel-Hamas war. While clashes remain largely contained, they have increased in intensity as Israel conducts a ground incursion in Gaza against Hezbollah ally Hamas.

The civilian deaths in Lebanon on Sunday were confirmed by a local civil defence official and Lebanese state-run media.

Israeli army spokesperson Avichay Adraee also said in a statement on Sunday that one Israeli was killed in a retaliatory attack by Hezbollah. He did not specify whether the person was a civilian or a soldier.

Hezbollah, a pro-Iranian Shia group, said it fired multiple Grad rockets at the northern Israeli town of Kiryat Shmona after the Israeli attack, saying it was in response to Israel’s “heinous and brutal crime”.

Hezbollah lawmaker Hassan Fadlallah said “the enemy will pay the price for its crimes against civilians”.

Israeli army spokesperson Daniel Hagari offered no apologies for the attack on the Lebanese family.

“Regarding Lebanon, we attack on the basis of intelligence information and we will continue to attack. That is our mission. Anyone who threatens us we will attack them,” Hagari said, before adding that Israel examines “every event that occurs in Lebanon”.

Samir Ayoub, a Lebanese journalist who was in the car in front of the one that was struck, said that the three girls killed were his sister’s children and the woman was their grandmother.

“There were no men in the car that was hit – there were three innocent young children with their grandmother and their mother,” he said. “Three children were burned in the car and no one could save them. And I pulled out their mother as she was screaming, ‘My children!’ Where are the terrorists? Israelis, you are the terrorists.”

While clashes between Israeli troops and Lebanon’s Hezbollah fighters remain largely contained to areas near the border, they have increased in intensity as Israel continues its ground incursion into Gaza.

There has been speculation that the front between will eventually escalate into full-blown war, but in a highly-anticipated speech on Friday, Hezbollah leader Hassan Nasrallah avoided any such declaration.

Complaint to the UN

Lebanon’s state-run National News Agency reported that two civilian cars carrying members of the same family – one of them a local journalist – were driving between the towns of Ainata and Aitaroun on Sunday evening when they were hit by an Israeli air strike.

One of the cars was hit directly and burst into flames, the report said. The three children killed were 10,12 and 14, it said. Their mother is severely injured.

Ali Safieddine, the head of the civil defence in the Tyre district in south Lebanon, confirmed that a woman and three children were killed.

Lebanon will submit a complaint to the United Nations over the killing of civilians, Foreign Minister Abdallah Bou Habib said. He said that Lebanon was collecting information and pictures and will likely submit its complaint on Monday.

Reporting from Naqoura in southern Lebanon, Al Jazeera’s Ali Hashem said it seemed Lebanon and Israel were “climbing the ladder of escalation gradually”.

“This is the first time that Hezbollah claims directly that it has launched rockets towards Israel since the start of the conflict. That means there will be an Israeli reaction,” he added.

Earlier Sunday, local Lebanese officials said an Israeli drone had struck near two ambulances on their way to pick up casualties from overnight strikes in southern Lebanon, wounding four paramedics.

The Israeli army said in a statement that it had launched strikes on a “terrorist cell” that was attempting to fire missiles toward Israel from the Ras Naqoura area in south Lebanon and had not intentionally targeted the vehicles.

Also Sunday, Hezbollah said in a statement that it had targeted an Israeli military vehicle across the border from the Lebanese town of Blida with guided missiles, killing and wounding members of the crew.

The death of the woman and three children raised the number of civilians killed on the Lebanese side in the border clashes to 14, while at least one Israeli civilian has been killed.

Hezbollah officials have warned that if Israel kills Lebanese civilians it will be considered a violation of the rules of engagement and it will retaliate by attacking civilian targets.