Israel's military said Sunday it has fired on Hezbollah targets in southern Lebanon over the past 24 hours, days into a fragile ceasefire between it and the Iran-backed Islamist group.

The military said in a statement that it acted to "remove threats" that violated "the ceasefire agreement conditions".

Among the incidents, the army said it identified "several armed terrorists adjacent to a church in southern Lebanon that was actively used by" Hezbollah on Saturday.

"The troops fired toward the terrorists and eliminated them," it said, adding that in a later scan of the area, troops "located a tunnel shaft containing weapons".

Lebanon's official National News Agency (NNA) reported "the continued violation of the ceasefire" in south Lebanon by Israeli forces on Sunday.

It reported a series of incidents, among them that "enemy warplanes launched a strike" early Sunday targeting the border village of Yarun.

It also said Israeli forces shelled several locations, including the town of Khiam and the outskirts of Aitarun, and reported "enemy automatic weapons fire" elsewhere.

Israel and Lebanon agreed to a US- and French-brokered truce that began at dawn on Wednesday after more than a year of cross-border exchanges of fire, and two months of all-out war, between Israel's military and Hezbollah.

The ceasefire has reduced the level of fighting over the past five days, but Israel has hit Hezbollah targets it says were violating the truce.

Visiting new military recruits on Sunday, Prime Minister Benjamin Netanyahu said Israel was "strictly enforcing the ceasefire agreement". 

He said "any violation would immediately be met with a powerful response".

In northern Israel, some residents cautiously returned to their homes this weekend, with media reporting that around 150,000 schoolchildren were able to resume classes in some communities in the north on Sunday.

But 16,000 students were unable to return to school in the north, the education ministry said.

Israel has said more than 60,000 people have been forced from their homes in the north for more than a year by the threat of Hezbollah rocket fire.

The Israel-Hezbollah war killed at least 3,961 people in Lebanon, according to the health ministry in Beirut, most of them after Israel stepped up its bombing campaign in September.

On the Israeli side, the hostilities killed at least 82 soldiers and 47 civilians, authorities said.