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"If necessary, I gave a directive to wage "an intensive war in the event of any breach of the truce," said Netanyahu.
The United States and France will ensure the deal is "fully implemented", said a joint statement.
The French presidency said discussions on a ceasefire had made significant progress.
This is militant group's heaviest barrage in several days, in response to deadly Israeli strikes in Beirut while negotiators pressed on with cease-fire efforts.
However, there was no immediate confirmation from Hezbollah.
Lebanese Prime Minister Najib Mikati instructed the foreign ministry to submit a complaint to the UN Security Council over the raid on the coastal town of Batroun.
He was appointed as Hezbollah's deputy chief in 1991 by the armed group's then-secretary general Abbas al-Musawi.
Safieddine had been running Hezbollah alongside its deputy secretary general Naim Qassem since Nasrallah's assassination.
Wafiq Safa, who heads Hezbollah's liaison and coordination unit responsible for working with Lebanese security agencies, was targeted by Israel.
Israeli military spokesman Daniel Hagari said Israel knew Safieddine was in Hezbollah's intelligence headquarters when fighter jets bombed it last week.
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