The Israel Defense Forces said it conducted an airstrike on a school in Gaza, in the northern city of Beit Lahiya, to target "terrorists who were operating inside a Hamas command and control center."

Four people were killed and 15 were wounded, according to Gaza Civil Defense.

The death toll in Gaza since Oct. 7 now stands at 41,595, according to the Gaza Ministry of Health.

Hezbollah confirmed on Sunday that Ali Karaki -- the commander of the militant group's southern front -- was among those killed alongside leader Hassan Nasrallah in an Israeli airstrike in southern Beirut on Friday.

Karaki fought for Hezbollah since 1982, Hezbollah said in a statement. Karaki was "responsible for leading the southern front with all its axes and units" in the group's cross-border fighting with Israeli forces that began on Oct. 8, the statement added.

The Israel Defense Forces reported Karaki's death on Saturday in a statement detailing the strike that killed Nasrallah.

-ABC News' Ghazi Balkiz and Victoria Beaule

Lebanon's caretaker Prime Minister Najib Mikati told reporters Sunday that some 1 million people may have been displaced amid Israel's strikes on Hezbollah.

"There are a million Lebanese people who have moved from one place to another, and this may be the largest displacement operation that has occurred," Mikati said.

Lebanon's total population as of 2022 was 5.5 million people, per World Health Organization data.

Israel's intense airstrike campaign has been especially punishing for Lebanese people living in Hezbollah heartlands, notably the south and east of the country as well the densely populated southern Beirut suburb of Dahiya.

Lebanese officials said Israeli strikes have killed at least 1,030 people in Lebanon since Sept. 16, when Israel detonated thousands of pager devices used by Hezbollah members. Israel detonated Hezbollah walkie-talkies the following day and then intensified its nationwide airstrike campaign.

Among those confirmed dead since Sept. 16 are 56 women and 87 children. Some 6,352 people have been wounded.

"The security forces will intensify their measures to protect shelters and the displaced and ensure peace and security in the regions and on the roads," Mikati said Sunday.

"We are following up on the issue of public health in shelters to avoid the spread of any diseases," the caretaker prime minister added.

"We are following up on the affairs of the displaced in full through the relevant ministries, and the state is doing everything necessary within its capabilities to secure the displaced."

"Thanks to all those who have embraced the displaced."

Lebanon's government, Mikati added, is "committed to a diplomatic solution to reach a ceasefire."

-ABC News' Ghazi Balkiz and Victoria Beaule

The Israel Defense Forces said in a Sunday morning statement that it "attacked hundreds of terrorist targets of the Hezbollah terrorist organization throughout Lebanon" over the previous 24 hours.

"The IDF continues to attack with force, damage and degrade Hezbollah's military capabilities and infrastructure in Lebanon," the force wrote on X.

Israel is continuing its intense air campaign following the decapitation strike that killed Hezbollah leader Hassan Nasrallah in Beirut on Friday.

Meanwhile, two U.S. officials told ABC News late Saturday that small-scale Israeli ground operations or "border movements" into Lebanon to attack Hezbollah positions in the frontier area began or were about to.

Cross-border Hezbollah fire continues despite the killing of many of its senior commanders.

The IDF said Sunday that approximately eight projectiles entered northern Israel "and fell in open areas."

An Israeli warship also intercepted a drone "that made its way to the country's territory in the Red Sea," the IDF wrote on X.

-ABC News' David Brennan