Israel’s military chief Eyal Zamir said fighting against Lebanese militant group Hezbollah, which began early Monday, could take "many" more days.

"We have launched an offensive campaign against Hezbollah," Zamir said in a video shared by the military on Monday, hours after rocket fire claimed by Hezbollah prompted a wave of Israeli strikes on Lebanon. "We must be prepared for several days of fighting, many."

Prime Minister Nawaf Salam condemned rocket fire launched at Israel on Monday, as the Israeli military launched a series of strikes across Lebanon in response.

"Regardless of who is behind it, the rocket fire from southern Lebanon is an irresponsible and suspicious act that endangers Lebanon’s security and safety and gives Israel pretexts to continue its attacks on it," Salam said on X.

Israeli strikes on Lebanon killed at least 31 people on Monday, authorities said, following rocket fire from Tehran-backed militant group Hezbollah after the killing of Iran's supreme leader.

Israel's military vowed to intensify its attacks on the country and make Hezbollah pay a "heavy price" after launching several strikes on Beirut's southern suburbs and south Lebanon, areas where Hezbollah holds sway.

The Israeli military told residents of about 50 towns and villages in Lebanon to evacuate on Monday, warning of imminent attacks against Hezbollah militants, following rocket fire at Israel.

"For your safety, evacuate your homes immediately and move at least 1,000 meters away from your village to open areas," an army spokeswoman said in a statement on X, listing localities in the country's south and east.

Projectiles fired from Lebanon triggered air raid sirens in northern Israel, the Israeli military said on Monday, adding it had intercepted one of them.

Lebanon and France postponed on Sunday an upcoming conference to support the Lebanese Army and security forces, a joint statement by both countries' presidencies said, citing unfavorable conditions in the region.

Thousands of Hezbollah supporters gathered in Beirut's southern suburbs to mourn Iran's supreme leader Ayatollah Ali Khamenei on Sunday, chanting "death to America, death to Israel" while crying over the killed figure.

Hezbollah vowed Sunday to confront the United States and Israel over their strikes on the group's key backer Iran.

"We will undertake our duty of confronting the aggression," Hezbollah chief Sheikh Naim Qassem said in a statement, adding that his group would not leave "the field of honor and resistance".

The U.S. ambassador to Lebanon informed the country that Israel had no intention of escalating hostilities as long as no attacks were launched from Lebanon, the Lebanese presidency said in a statement.

The message came as Lebanese authorities fear Iran-backed Hezbollah could become embroiled in renewed conflict with Israel after the U.S. and Israel bombed Iran on Saturday and Tehran responded with missile attacks.

Lebanon's Iran-backed Hezbollah called on Saturday for the Middle East to stand against Israel and the United States' attack on Iran.