Lebanon's government has decided on an "immediate ban" of Iran-backed Hezbollah's military and security activity, Prime Minister Nawaf Salam said Monday, in an unprecedented move as Israel retaliated to rocket fire.

Israel's military said Monday there was no reason to launch a ground invasion of Lebanon "imminently" after an overnight attack from Hezbollah prompted Israel to retaliate with air strikes.

"There is nothing on the ground that constitutes going into ground invasion.. imminently," military spokesman Lieutenant Colonel Nadav Shoshani told journalists on whether Israel would send troops in Lebanon.

Israel's military said Monday it struck a senior Hezbollah operative in Beirut, with the defense minister saying the Lebanese group's chief Naim Qassem is "a marked target".

"A short while ago, the (Israeli military) precisely struck a senior Hezbollah terrorist in Beirut," the military said. AFPTV showed smoke rising from the southern Beirut district of Dahieh, a stronghold of Hezbollah.

Iran’s army said Monday it targeted US Ali Al Salem air base in Kuwait as well as vessels in the Indian ocean after the killing of the Islamic republic’s supreme leader in U.S. and Israeli strikes.

"Missile units of the army’s ground and naval forces operating from various locations targeted the U.S. Ali Al Salem air base in Kuwait as well as enemy vessels in the northern Indian Ocean over the past hours," the army said in a statement.

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."

Israel and Hezbollah traded fire on Monday, while President Donald Trump vowed to avenge the deaths of U.S. service members and said the war with Iran could last for weeks.

The European Union has warned of the cost to the Middle East of a long war, and said it was reinforcing its naval mission in the Red Sea.

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.