The projectiles launched by the Lebanese militant group on Monday were the first since the start of US and Israeli strikes on Iran.
The Shi'ite Muslim group said it launched the attack against Israel in response to Israel killing Khamenei and continuous Israeli violations against Lebanon.
"The resistance leadership has always emphasised that the continuation of Israeli attacks and the assassination of our leaders, youth, and people gives us the right to defend ourselves and respond at the appropriate time and place," Hezbollah said in a statement.
The Israeli military said it intercepted a projectile that crossed the border and several others fell in open areas. No injuries or damage were reported.
"In response to projectile fire toward northern Israel, the IDF is striking Hezbollah targets across Lebanon," it said on X on Monday.
Explosions were heard in the Lebanese capital Beirut and Lebanese security sources told Reuters that Israel had struck Beirut's southern suburbs, a Hezbollah stronghold.
The encounter came after Israel launched a new wave of strikes on Tehran and Iran responded with more missile barrages, a day after the killing of Khamenei that's spiralled the Middle East and the global economy into deepening uncertainty.
US and Israeli strikes - and Iranian retaliation - sent shockwaves through sectors from shipping to air travel to oil, amid warnings of rising energy costs and disruption to business in the Gulf, a strategic waterway and global trade hub.
US President Donald Trump said the attack on Saturday was intended to ensure Iran could not have a nuclear weapon, to contain its missile program and to eliminate threats to the United States and its allies.
As the first US casualties were reported, and with the vital Strait of Hormuz closed and the glittering Gulf cities of Dubai, Abu Dhabi and Doha under bombardment, the scale of the risk taken by Trump in launching the attack was becoming clearer.
Only around one in four Americans approve of the operation, according to a Reuters/Ipsos poll, and if Hormuz, which is the passage for about 20 per cent of world oil supplies, remains closed for more than a few days, squeezed US consumers will start to feel the pressure on prices at the pumps.
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, prompting sharp jumps in crude oil prices on Monday.
Global air travel was also heavily disrupted as continued air strikes kept major Middle Eastern airports, including Dubai closed in one of the biggest aviation interruptions in years.
Iran's President Masoud Pezeshkian said a leadership council composed of himself, the judiciary head and a member of the powerful Guardians Council had temporarily assumed the duties of Supreme Leader.
But it remained unclear what the longer-term prospects were for Iran to rebuild its leadership.
Israel claimed responsibility for killing Khamenei, in what it said was a "precise, large-scale operation" guided by intelligence, while he was in his central leadership compound in the heart of Tehran.
It said it aimed to dominate the skies over Tehran, giving no sign of planning an end to the biggest aerial operation in its history, involving hundreds of fighter jets.
"We have the capabilities and the targets to keep going on for as long as necessary," Israeli military spokesperson Lieutenant Colonel Nadav Shoshani said.
But as Iran fired renewed missile barrages across the region, Israel's ambulance service said nine people were killed in the town of Beit Shemesh, the United Arab Emirates said Iranian attacks killed three people and Kuwait reported one dead.
Three US service personnel were also killed and five seriously wounded, the first American casualties of the operation, the US military said.
Trump said on social media the US military had destroyed nine Iranian warships so far and was "going after the rest".
Inside Iran, some grieved for Khamenei while others celebrated his death, exposing a deep fault line in a country stunned by the sudden demise of the man who ruled for decades.
Footage from Tehran showed mourners packed into a square, dressed in black and many of them weeping.
But videos posted on social media also showed joy and defiance elsewhere, with people cheering as a statue was toppled in the city of Dehloran in Ilam province, dancing in the streets of Karaj city, near Tehran in Alborz province, and celebrating in the streets of Izeh in Khuzestan province.
with AP
