Despite a US-brokered ceasefire with Hezbollah agreed in June, the Israeli military is operating in what it has declared as a security zone in southern Lebanon.
Lebanon's health ministry said on Sunday two men were killed in a town on the edge of the zone occupied by Israeli troops, while the two women were killed in Arab Salim, which sits well north of the occupied area.
The Israeli military had issued an online evacuation warning early on Sunday for areas near a building in Arab Salim that it said it would strike because it was being used by Hezbollah.
Two girls were among six others injured in that strike.
Lebanese President Joseph Aoun's office called Sunday's strikes, which it said destroyed a hospital and damaged a finance ministry building, "a dangerous escalation" that targeted "purely civilian administrations and health centres".
"President Aoun held the Israeli side fully responsible for this ongoing escalation, calling on the United States and the international community to take immediate action to stop these violations and hold the perpetrators accountable," it said.
The Israeli military said its targets included what it described as Hezbollah weapons storage facilities and a command centre inside a building previously used as a hospital.
It also said it used precision munitions and aerial surveillance to mitigate civilian harm.
Sunday's evacuation warning was only the second issued since the June ceasefire announcement.
The first online evacuation order came on August 5 for residents of Mansouri, near Tyre, although Israel had already dropped leaflets on the village just a week into the ceasefire, telling residents to leave ahead of strikes.
Four people were killed and 23 injured across southern Lebanon on Friday, the health ministry said on Saturday, in Israeli strikes launched without evacuation warnings.
The Israeli military said those strikes hit Hezbollah weapons storage facilities.
Hezbollah said on Saturday Israel's continued escalation aimed to pressure the Lebanese government, which has been engaged in direct talks with Israel under US auspices - negotiations that the Iran-backed group has rejected.
Israeli strikes in Lebanon have killed more than 4300 people since March 2, when Hezbollah fired at Israel in support of Iran.
