Tehran, Iran - The US said airstrikes on Sunday aimed to "punish" Iran over the first US military deaths since renewed hostilities with the Islamic republic.

Iran rapidly announced its own retaliation, saying two US bases in Kuwait were targeted in response to more than a week of intensifying attacks – which Tehran said included strikes on an airport, a railway station, and bridges.

A preliminary deal aimed at ending the war has collapsed as the foes fight to break the deadlock over the Strait of Hormuz, a waterway key to the world's oil supply.

The Iranian army announced on Sunday it targeted two US bases in Kuwait with drones, hitting an ammunition depot at Camp Udairi and Patriot radar and air surveillance systems at the Ali Al Salem Air Base.

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Tehran had also launched fresh strikes in Jordan, where the US military's Central Command (CENTCOM) said two service members were killed Friday as they "defended against Iranian ballistic missile and drone attacks."

It said another service member was still missing in action.

Those deaths brought to 16 the confirmed number of US military fatalities since US-Israeli strikes started the war on February 28.

The US military said that it carried out an eighth consecutive night of strikes against Iran, with targets including units behind the attack that killed two American troops in Jordan.

The attacks aimed to "swiftly punish Islamic Revolutionary Guard Corps forces who launched attacks against American service members in Jordan last night", said US Central Command.

The Iranian news agencies Fars and Tasnim simultaneously reported US attacks on Sirik, a port located on the Strait of Hormuz in southern Iran.

Iranian supreme leader Mojtaba Khamenei, who took over from his father after he was killed in the opening salvo of US-Israeli strikes, vowed to teach the Americans an "unforgettable lesson", in a statement carried by state TV.

Major General Mohsen Rezaei, a senior military adviser to Khamenei, warned that Tehran would resume "full-scale offensive operations" if US strikes continued in the coming days.

And Iran's central military commander, Ali Abdollahi, warned that further US aggression would face a "decisive and devastating response", according to a statement carried by state television on Sunday.