The Israeli military says it has struck Hezbollah targets “deep inside Lebanese territory”.
Weapons caches and “terrorist infrastructure” were hit, the military said.
The areas affected were Chabriha, Borj El Chmali, Beqaa, Kfarkela, Rab El Thalathine, Khiam, and Tayr Harfa, it added.
Iran, which backs Hezbollah, has subsequently warned Israel against any new “adventure” in Lebanon.
Benjamin Netanyahu, Israel’s prime minister, had warned Hezbollah it would “pay a heavy price” for an attack on a football pitch in the Israeli-occupied Golan Heights in which 12 people including children were killed, Israeli authorities said.
Hezbollah said it had “absolutely nothing to do with the incident” but Israel’s foreign ministry said it was “unequivocally responsible”.
The Israel Defence Forces said the rocket was launched from an area north of the village of Chebaa in southern Lebanon.
Forensics showed it was an Iranian-made Falaq-1, IDF spokesman Daniel Hagari said.
Families mourn children killed on a football pitch. Pic: Reuters
Mr Netanyahu, who cut short a trip to the US after hearing about the attack, said Hezbollah would pay a price “it has thus far not paid”.
Israel Katz, the foreign minister, told Israeli broadcaster Channel 12 that Hezbollah had “crossed all the red lines here”.
“We are nearing the moment in which we face an all-out war,” he added.
The United States said its support for Israel’s security was “iron-clad and unwavering against all Iranian-backed terrorist groups, including Lebanese Hezbollah”.
At least 12 killed in rocket attack
The Israeli ambulance service said 13 people were wounded in the attack on the football pitch – filled at the time with children and teenagers.
“The scene was gruesome,” Idan Avshalom, a medic with the service said.
“They were playing soccer – they heard sirens [and] ran to the shelter,” said witness Mourhaf Abu Saleh.
“But they couldn’t reach the shelter because the rocket hit the site between the ground and the shelter.”
It was the deadliest attack on Israeli civilians since Hamas fighters paraglided over the border from Gaza into southern Israel to carry out their 7 October massacre of 1,200 people, Mr Hagari said.
The attack by Hamas, the Iran-backed militant group ruling Gaza, triggered Israel’s offensive on the besieged enclave.
According to local health officials in Gaza, more than 39,000 people have been killed in the almost 10-month war.
That count does not distinguish between civilians and Hamas fighters.
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Earlier on Saturday, an Israeli airstrike hit a school in central Gaza, killing at least 30 people, including seven children, Palestinian health officials said.
The Hamas-run health ministry said another 100 people were wounded.
Israel’s military said it targeted a Hamas command centre which it claimed was embedded inside the school.
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Israel and Hezbollah have been trading fire since 8 October.
In recent weeks, the exchange of fire along the Lebanon-Israel border has intensified, with Israeli airstrikes and rocket and drone attacks by Hezbollah striking deeper and further away from the border.
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