Earlier, rockets were fired from Lebanon into Israel, for the second time since December, sparking concern about whether the fragile ceasefire would hold.
In a statement on Saturday, Hezbollah denied being responsible for the attack, saying that it was committed to the truce and accused Israel of blaming it for the strikes as a pretext for more attacks.
Israel's army said the intercepted rockets targeted the Israeli town of Metula.
An Israeli official said six rockets were fired and three crossed into Israeli territory and were intercepted.
The official said Israel could not confirm the identity of the group that fired the rockets.
Lebanon's state-run National News Agency said a strike in the southern village of Touline killed five people, including a child, and wounded 11 others, including two children.
On Saturday night, Israel again struck Hezbollah targets in Lebanon.
A strike hit a garage in the coastal city of Tyre, the NNA reported, with one person killed and seven wounded.
It was the first time the city had been struck since the ceasefire took effect.
And a strike on Hawsh al-Sayed Ali village along the border with Syria wounded five people, according to the NNA.
Hezbollah began launching rockets, drones and missiles into Israel the day after Hamas' October 7, 2023, attack out of Gaza ignited the war there.
The Israel-Hezbollah conflict boiled over into an all-out war in September as Israel carried out massive waves of air strikes and killed most of the militant group's senior leaders.
The fighting killed more than 4000 people in Lebanon and displaced about 60,000 Israelis.
Under the ceasefire reached in November, Israeli forces were supposed to withdraw from all Lebanese territory by late January.
The deadline was then extended to February 18 by agreement between Lebanon and Israel.
But since then, Israel has remained in five locations in Lebanon, across from communities in northern Israel, and has carried out dozens of air strikes on southern and eastern Lebanon, saying it attacked Hezbollah, while continuing targeted drone attacks that have so far killed several members of the militant group.
Lebanon has appealed to the UN to pressure Israel to fully withdraw from the country.
Israel's Prime Minister's office said on Saturday it instructed the army to act forcefully against dozens of targets in Lebanon, adding: "Israel will not allow any harm to its citizens and sovereignty."
Israel's army said Saturday it was carrying out strikes on Hezbollah targets in south Lebanon and that it struck dozens of the group's rocket launchers and a command centre where Hezbollah was operating.
In a statement, Lebanon's Prime Minister Nawaf Salam asked the Lebanese military to take all necessary measures in the south but said the country did not want to return to war.
The United Nations Interim Force in Lebanon, known as UNIFIL, said it was alarmed at the possible escalation of violence and urged all parties to avoid jeopardising the progress made, saying further escalation could have serious consequences for the region.
The strikes come a day after Israel said it would carry out operations in Gaza "with increasing intensity" until Hamas frees the 59 hostages it holds — 24 of whom are believed alive.
Late Friday night, Israeli strikes killed at least nine people, including three children, in a house in Gaza City, according to Al-Ahly Hospital, which received the bodies.
