Israel said it was attacking sites connected to Lebanon's Shi'ite Muslim armed group Hezbollah, one of Tehran's principal allies in the Middle East, after Hezbollah acknowledged launching missiles and drones towards Israel in retaliation for the killing of Iran's Supreme Leader Ali Khamenei.
The Israeli military said it intercepted a projectile launched from Lebanon, while others landed in open areas of the country.
Israel carried out air strikes on the Hezbollah-controlled southern suburbs of Beirut on Monday, with more than a dozen explosions rocking the Lebanese capital. Israel said it also struck senior Hezbollah militants near Beirut.
People fled on foot and by car in Beirut, clogging the roads, after the series of strikes began in the early hours before dawn.
The Hezbollah and Israel tit-for-tat attacks widen the conflict that has spread through the Middle East since the US and Israel attacked Iran on Saturday, sending oil prices soaring and snarling air travel.
Lebanon's presidency said on Saturday it had been told by the US ambassador that Israel would not escalate against Lebanon as long as there were no hostile acts from the Lebanese side.
The Israeli military said Hezbollah was "fully responsible for any escalation" and warned residents of dozens of villages in southern and eastern Lebanon to evacuate.
The Israeli military said late on Sunday its air force had established aerial superiority over Tehran, and a wave of strikes across the capital had targeted intelligence, security, and military command centres.
In Iran, President Masoud Pezeshkian said a leadership council composed of himself, the judiciary head and a member of the powerful Guardian Council had temporarily assumed the duties of Supreme Leader.
Air raid sirens sounded across Israel late on Sunday, including in Tel Aviv where projectiles were seen streaking across the night sky as Iran fired new barrages of missiles.
The first US casualties of the campaign, including the deaths of three service personnel were confirmed on Sunday. Two US officials, speaking on condition of anonymity, told Reuters the US service members were killed on a base in Kuwait.
Trump paid tribute to the three killed as "true American patriots" but warned there will likely be more casualties.
"That's the way it is," he said.
An extended military campaign could pose a major political risk for Trump's Republican party ahead of US midterm elections that could decide the fate of Congress. Only around one-in-four Americans approve of the operation, according to a Reuters/Ipsos poll.
But in a video posted on Sunday, Trump vowed military strikes on Iran will continue until "all our objectives are achieved".
He said the assault had so far wiped out Iran's military command and destroyed nine Iranian navy ships and a naval building.
American aircraft and warships have struck more than 1000 Iranian targets since the start of major combat operations on Saturday, the US military said.
Trump called on Iran's military and police, including the powerful Islamic Revolutionary Guards Corps, to stop fighting, promising immunity for those who surrender and threatening "certain death" for those who resist.
"I call upon all Iranian patriots who yearn for freedom to seize this moment, to be brave, be bold, be heroic and take back your country," Trump said in the pre-recorded video.
"America is with you."
Trump said the military campaign against Iran could continue for at least four weeks.
Following the death of Khamenei, Iran faces a power vacuum that could leave it in chaos, but the Trump administration has not outlined longer-term aims for the country.
Iran's Revolutionary Guards said they had hit three US and UK oil tankers in the Gulf and the Strait of Hormuz, and attacked military bases in Kuwait and Bahrain with drones and missiles.
Shipping data showed hundreds of vessels including oil and gas tankers dropping anchor in nearby waters with traders expecting sharp jumps in crude oil prices on Monday.
Global air travel was also heavily disrupted as continued air strikes kept major Middle Eastern airports closed, including Dubai - the world's busiest international hub - in one of the biggest aviation interruptions in recent years.
with AP
