Before the strikes on Saturday, Iran's supreme leader said Washington would pay for "seeking to escalate the conflict".
US Central Command said in a statement that the airstrikes began at 6pm (8am Sunday AEST) at President Donald Trump's direction.
"The strikes are designed to further degrade Iran's ability to threaten commercial shipping in the Strait of Hormuz and swiftly punish Islamic Revolutionary Guard Corps forces who launched attacks against American service members in Jordan last night," it said, without providing further details.
Iran's Mehr news agency said the US carried out an attack near Sirik in southern Iran, adding that no casualties or damage to infrastructure have been reported.
The US and Iran have intensified attacks since an interim ceasefire deal signed a month ago fell apart last week, raising the possibility of a return to all-out war.
Central Command said the two deaths occurred on Friday and that a third US service member was missing in action. The announcement brought the number of US service members killed since the war began to 16, while more than 420 have been wounded.
US Defense Secretary Pete Hegseth posted on X: "Godspeed, heroes. Their sacrifice only stiffens our resolve."
Iran appeared to target Saudi Arabia as well as other US Gulf allies and Jordan on Saturday after US attacks on Iranian bridges, power facilities and other infrastructure.
In a written statement carried by the official social media accounts of Iran's supreme leader and Iranian state media, Supreme Leader Ayatollah Mojtaba Khamenei said repeated US breaches of the interim deal had shown that Trump's signature was "utterly worthless and devoid of credibility".
"Now that the American enemy is seeking to escalate the conflict thereby incurring even heavier costs and further humiliation, it should know that the noble nation of Iran and the Resistance Front have unforgettable lessons in store for it," the statement said.
The White House did not immediately respond to a request for comment.
Khamenei's whereabouts remain a mystery. The conflict, which began when the US and Israel launched strikes on Iran at the end of February hoping to disable its missile program and its regional proxies, has led to major disruption to energy supplies, fears over global inflation and a battle for control of the Strait of Hormuz.
On Saturday, Kuwait came under sustained attack, with the armed forces saying they had intercepted Iranian ballistic missiles and drones, and that some firefighters and oil sector workers had been injured while responding to the attacks.
Iran's IRGC said it had struck a US military support centre at Kuwait's Camp Arifjan and destroyed a radar facility at Ali Al Salem Air Base. Kuwait Petroleum Corporation later said one of its oil facilities had been hit in "repeated Iranian attacks", causing significant damage and some injuries, according to the state news agency.
As well as hitting Kuwait, the IRGC targeted a site in Bahrain where US combat aircraft were gathered at Sheikh Isa Air Base and an intelligence data centre, Iranian media said.
The Guards also destroyed at least two US fighter aircraft and three other aircraft during a missile and drone attack early on Saturday on the US base in Al Azraq, Jordan, according to Iranian state TV.
Saudi Arabia's early warning system issued alerts early on Saturday urging residents of Al-Kharj and Yanbu to seek shelter. Al-Kharj, east of Riyadh, is home to a military base that hosts US troops, while Yanbu, on the Red Sea, has a key oil export terminal.
Two people briefed on the matter said an Iranian missile attack, the first on Saudi Arabia in more than three months, had triggered the alerts. Saudi state media did not say what had prompted the alerts and the government media office did not respond to a request for comment.
The IRGC made no mention of any attack on Saudi Arabia.
Earlier, US Central Command said it had hit Iranian surveillance sites, military logistics infrastructure, underground weapons storage and maritime capabilities.
US airstrikes early on Saturday killed three people and wounded eight others in the southern Hormozgan province, which borders the Strait of Hormuz, while two bridges and a road tunnel were damaged, Iranian state TV reported.
The US carried out further airstrikes in the same province on Saturday afternoon, the semi-official Fars news agency said, quoting provincial authorities.
Iran's Health Ministry said on Saturday that 50 people had been killed and more than 500 wounded in US strikes on the country over the past three weeks.
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