It reported no casualties but accused Hezbollah of a “blatant violation.”
Israel this week said it had captured the Nabatieh-area Ali al-Taher ridge, which it considers part of its self-declared “security zone” in south Lebanon.
Hezbollah, which has not claimed any attacks for weeks, has not commented on Israel’s declaration of control over the site.
Aoun said Sunday’s strikes, which damaged government premises and destroyed an out-of-service hospital, were “a dangerous escalation... reaching Lebanese state institutions” and health facilities.
He called on the international community — particularly the United States, which has sponsored direct Israel-Lebanon talks and a framework agreement between the sides in June — “to urgently act to stop these violations.”
Lebanon’s health ministry said two people were killed in strikes on south Lebanon’s Nabatieh al-Fawqa, with two women also killed in nearby Arab Salim.
It said 20 other people including several women and three children were wounded there, as well as in the city of Nabatieh and town of Kfar Rumman.
The ministry later reported that a strike on a parking lot near Nabatieh killed three more people.
The ministry said one of the strikes in Nabatieh al-Fawqa “totally destroyed” the out-of-service Ghandour hospital, decrying “another grave violation of international humanitarian law.”
Israel’s army said it targeted Hezbollah operatives and infrastructure, including “weapons storage facilities and terrorist structures,” as well as “a Hezbollah command center that had been established inside a building previously used as a hospital.”
It had earlier issued its first evacuation notice in Lebanon in a month, warning residents near a building it called a Hezbollah facility in Arab Salim to leave ahead of an attack on the site.
It did not issue warnings for other areas where strikes were reported.
Lebanon’s state-run National News Agency said that after the Israeli warning for Arab Salim, “enemy warplanes launched a strike on another house, destroying it” and killing the two women.
It said the Israeli military subsequently carried out a strike on the building threatened in the evacuation warning.
At the scene of the second strike, an Agence France-Presse (AFP) correspondent saw the ruins of a devastated villa, with large decorative columns laying on their side next to stairs littered with rubble.
Haidar Haidar, the brother of the building’s owner, told AFP that nobody had been living inside.