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.
Kuwait's military later said it was responding to another round of Iranian drone and missile strikes, while sirens sounded in Bahrain.
Tehran had also launched fresh strikes in Jordan, where the US military's Central Command 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 28 February.
The US military said it carried out an eighth consecutive night of strikes against Iran, with targets including units behind the attack that killed the 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.
'Unforgettable lesson'
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.
The renewed violence was initially sparked by Iranian attacks on ships in the strategic Strait of Hormuz.
Iran closed the strait after the war broke out, and control over the route has become leverage in negotiations with Washington.