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

Small-scale operations or "border movements" into Lebanon to take out Hezbollah positions right on the border have begun or are about to, according to two U.S. officials.

Israel does not yet appear to have fully decided whether to launch a ground operation but is prepared for one, the officials said. If a ground operation happens, its scope will likely be limited, sources said. The key is fulfilling the promise to Israelis that the tens of thousands displaced from northern Israel will be able to go home. To do that, decapitating Hezbollah is not enough, the officials said.

U.S. officials received a "few minutes notice" at best, before Hassan Nasrallah's assassination on Friday, the officials said.

In response to reports that Defense Secretary Lloyd Austin blew up when Israeli Defense Minister Yoav Gallant informed him about Nasrallah, the officials said, "We do bear a lot of risks" in the region, and their people were not given a lot of notice to prepare for possible hostile responses to the assassination, which did not please U.S. officials.

One of the officials noted that there is tolerance right now and that U.S. "interests in the region could be badly harmed" if U.S. officials lose their contacts with the Israelis.

The sources said Nasrallah, until the very end, had demanded a Hezbollah ceasefire be tied to a Gaza cease-fire.

Diplomacy remains the only viable long-term solution, even if a military campaign sets the stage for it, officials said.

-ABC News' Matt Gutman

President Joe Biden reiterated his message calling for a ceasefire Saturday when pressed by reporters for more reaction from the Israeli strike targeting Hezbollah's leader as he left church in Rehoboth Beach, Delaware.

When asked whether a ground incursion into Lebanon was inevitable now, Biden only said, "It is "time for a cease-fire."

When asked how the U.S. will respond to attacks on the U.S. warships in the Red Sea, Biden only said "We’re responding."

-ABC News' Michelle Stoddart

Israel Prime Minister Benjamin Netanyahu said that the assassination of Hezbollah leader Hassan Nasrallah "settled accounts" for those who had a hand in killing.

"The elimination of Nasrallah is a necessary condition for achieving the goals we have set: Returning the residents of the north safely to their homes, and changing the balance of power in the region over the years, because as long as Nasrallah lives, he would quickly restore the capabilities we took away from Hezbollah," Netanyahu said in a video message Saturday.

Netanyahu said he came to the decision that what Israel had done to Hezbollah was "not enough" earlier this week when he gave the order to assassinate Nasrallah. But, he warned that Israel's work is "not complete."

"The work is not yet complete. In the coming days we will face significant challenges ... There is no place in Iran or the Middle East that the long arm of Israel will not reach, and today you already know how true this is," Netanyahu said.

"We are determined to continue to strike at our enemies, return our residents to their homes, and return all our abductees," Netanyahu said.

-ABC News' Jordana Miller