Earlier, rockets were fired from Lebanon into Israel on Saturday, for the second time since December, sparking concern about whether the fragile ceasefire with the Lebanese militant group Hezbollah would hold.
Israel had said on Saturday that it would respond "severely" to the attack from Lebanon early on Saturday morning, when rockets were fired into northern Israel.
Israel's army said the intercepted rockets targeted the Israeli town of Metula.
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.
Lebanon has appealed to the United Nations to pressure Israel to fully withdraw from the country.
The Israeli 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 it was carrying out strikes on Hezbollah targets in south Lebanon.
There was no immediate comment from Hezbollah.
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 on 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.
Israel's military said on Friday its forces were planning fresh assaults into three neighbourhoods west of Gaza City and issued warnings on social media for Palestinians to leave the areas.
About 600 Palestinians have been killed since Israel relaunched the war earlier this week.
Israel had already cut off the supply of food, fuel, and humanitarian aid to Gaza's roughly two million Palestinians, aiming to pressure Hamas over ceasefire negotiations.
The international community has condemned the resumed attacks, with the foreign ministers of the United Kingdom, France and Germany calling Israel's strikes in Gaza a dramatic step backward.
The attack by Hamas-led militants in 2023 killed some 1200 people and took 251 hostages.
Most of the hostages have been freed in ceasefire agreements or other deals.
Israeli forces have rescued eight living hostages and recovered the bodies of dozens more.
Israel's retaliatory offensive has killed more than 49,000 Palestinians, according to the Gaza health ministry.
Israel says it has killed about 20,000 militants, without providing evidence.
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