Hezbollah condemned on Monday the government's decision to ban its military activities, while Israel carried out retaliatory strikes in response to rockets fired by the Iran-backed group.

In a statement, Mohammad Raad, the head of the group's parliamentary bloc, condemned Beirut's "swaggering decisions", saying that "the Lebanese were expecting a decision rejecting the (Israeli) aggression".

The war launched by the United States and Israel against Iran spread across the Middle East and beyond on Monday, with Lebanon's Hezbollah entering the fray and a British air base in Cyprus targeted.

The U.S. Embassy in Lebanon renewed its call for citizens to leave Lebanon immediately as the Middle East war expanded to Lebanon.

Several strikes hit Beirut's southern suburbs on Monday after Israeli evacuation warnings, as Israel attacked the country following Hezbollah's dawn missile launches.

The Israeli military said it killed the head of Hezbollah's intelligence services, Hussein Moukalled, in a strike in Dahieh overnight.

"The IDF now confirms that in a precise strike in Beirut last night (Sunday), the terrorist Hussein Moukalled, who served as the head of Hezbollah's intelligence headquarters, has been eliminated," the army said in a statement on Monday.

Israeli Defense Minister Israel Katz warned Monday that Israel would send Hezbollah chief Naim Qassem to "the bottom of hell" like Iran's supreme leader Ayatollah Ali Khamenei, after an attack by the Lebanese armed group.

"We will strike Hezbollah hard, and Naim Qassem, chairman of the Hezbollah terrorist organization, will discover that whoever follows Khamenei's path ends up like Khamenei -- at the bottom of hell," Katz said during a visit to the Israeli air force operations center.

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.