TEL AVIV—Israel warned residents of Lebanon to evacuate from places near where Hezbollah stores its weapons as its military intensifies attacks against the militant group.

The Israeli military launched a series of airstrikes in Lebanon on Monday morning in what it said was a pre-emptive assault targeting Hezbollah’s military infrastructure. Dozens of airstrikes hit Lebanon, according to the country’s state news agency. Israeli military spokesman Daniel Hagari said the airstrikes would continue in the near term and told residents of southern Lebanon to stay away from areas that would be targeted.

“We advise civilians from Lebanese villages located in and next to buildings and areas used by Hezbollah for military purposes, such as those used to store weapons, to immediately move out of harm’s way for their own safety,” Hagari said.

Hezbollah has fired some 150 projectiles at northern Israel in the past 24 hours, according to the Israeli military. More than 8,800 rockets, missiles and drones have been fired by Hezbollah into Israel since Oct. 8, according to Israel.

The recent round of Israeli strikes, which intensified this weekend, come amid escalating tensions between Israel and Hezbollah starting last week after a series of shocking blows to the U.S.-designated terrorist group. Israel’s recent attacks on Hezbollah include a strike on Friday that killed Ibrahim Aqil, the head of Hezbollah’s elite Radwan Force and other Hezbollah commanders, and a series of explosions of walkie-talkies and pagers last week. The recent escalation is raising concerns of all-out war between the two sides, which had previously engaged in tit-for-tat strikes across the border.

Hezbollah has said that since October, more than 500 of its fighters have been killed by Israel, alongside about 150 civilians, according to Lebanese authorities.

Tens of thousands of Israelis and Lebanese have evacuated from their homes on both sides of the border as a result of the fighting.

Israel recently added a new official war goal: ensuring that some 60,000 evacuated residents of northern Israel can return to their homes. It says it is trying to do so by pushing Hezbollah back from the border and degrading Hezbollah’s military capabilities. Hezbollah says that its attacks against Israel since Oct. 8 are in solidarity with Palestinians in Gaza and that it will stop firing on Israel when the conflict ends in Gaza , where tens of thousands of Palestinians have been killed.

Israel launched its war against Hamas in Gaza after the Hamas-led Oct. 7 attacks in southern Israel in which approximately 1,200 people were killed and around 250 taken hostage.

The U.S. State Department on Sunday urged American citizens to leave Lebanon while commercial travel options remain available. It also said that those who choose to remain should be prepared to shelter in place if the situation deteriorates further.

—Omar Abdel-Baqui contributed to this article.

Write to Anat Peled at anat.peled@wsj.com