Tel Aviv: Israel said that Hezbollah will "pay the price" after a rocket attack at Golan Heights killed 12 children, for which Tel Aviv blamed the Lebanese group, CNN reported on Sunday.

This has further sparked fears that an all-out war would envelop the region.

Hezbollah has "firmly" denied the allegations that it was behind the strike, the deadliest to hit Israel or Israeli-controlled territory since the October 7 attacks.

Israeli warplanes conducted airstrikes against Hezbollah targets "deep inside Lebanese territory" and along the border overnight Sunday, the Israeli military said in a statement from the military on Sunday morning. But, it was not immediately clear whether there were any casualties from those strikes.

Israel's Defence Minister Yoav Gallant pledged a heavy response, during a visit to the town of Majdal Shams near the Syrian and Lebanese borders, where the rocket attack left children and teenagers dead on Saturday.

"Hezbollah is responsible for this and they will pay the price," Gallant said. In an earlier statement from his office, he added: "We will hit the enemy hard."

The Saturday attacks on the region involved "approximately 30 projectiles" crossing from Lebanon into Israeli territory. Israel's military quickly blamed the Iran-backed group for the attack.

According to Prime Minister Benjamin Netanyahu's office, the attack killed 12 children and left 44 people injured. The children killed in the strike had been playing on a soccer field, CNN reported.

US Secretary of State Antony Blinken on Sunday backed Israel's assessment, saying "every indication" suggested the strike was a rocket fired by Hezbollah.

Some 20,000 Druze Arabs live in the Golan Heights, an area Israel seized from Syria in 1967 during the Six-Day War and annexed in 1981. Considered occupied territory under international law and UN Security Council resolutions, the area is also home to about 25,000 Israeli Jewish settlers, according to CNN.

Israel and Hezbollah have been trading rocket fire on an almost daily basis since the deadly October 7 attack on Israel by Hamas, and those exchanges have become increasingly volatile, sparking fears on several occasions that Israel's war with Hamas in Gaza would spiral into a conflict on multiple fronts across the Middle East.

While Hezbollah admitted striking the Golan Heights on Saturday, it rejected responsibility for the attack on Majdal Shams.

"We confirm that the Islamic Resistance has no connection to the incident whatsoever and firmly denies all false claims in this regard," a statement read.

(With Agency Inputs)