Kuwait came under sustained attack, with a desalination plant hit and operations at Kuwait International Airport suspended due to repeated missile and drone threats.
Iran's Islamic Revolutionary Guard Corps said it had struck a US military support centre at 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.
Kuwait's armed forces said they had intercepted Iranian ballistic missiles and drones early on Saturday, adding that a number of firefighters and oil sector workers had been injured.
Iran was responding to US strikes targeting bridges, power facilities and other infrastructure.
"Since there is no international institution to prevent the savagery of the US military, we have no path before us except the Quranic command: 'Whoever attacks you, attack them in the same manner'," the IRGC said in a statement warning US allies in the region to expect more strikes.
The IRGC targeted a site in Bahrain where US combat aircraft were gathered at Sheikh Isa Air Base and an intelligence data centre, Iranian state media reported.
The Guards said they had 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.
Reuters was not able to verify the reports.
Oil prices climbed more than four per cent on Friday to their highest level in more than a month, adding to political pressure on US President Donald Trump as his Republican Party tries to hold on to power in November congressional elections.
Washington and Tehran have been testing the limits of escalation since their ceasefire agreement fell apart last week, raising the prospect of a return to all-out war.
On Friday, both sides took aim at shipping traffic, with the US saying it was enforcing a naval blockade while Iran said it targeted vessels that violated its rules on navigating the Strait of Hormuz, the vital waterway for one-fifth of the world's oil supply.
Iranian media reported that several missiles had struck power facilities and desalination pumps in the southern city of Jask on Saturday, citing a local official.
Some 10,000 people in 20 villages were without water, Tasnim news agency reported.
A power generation and water desalination plant in Kuwait was hit in an Iranian attack, the country's energy and water ministry said.
It was the second attack on Kuwaiti water desalination sites in two days.
Kuwait's foreign ministry said Iran's targeting of vital infrastructure endangered civilians and violated international law, adding it held Tehran fully responsible for the attacks.
The US military's Central Command said earlier it concluded its seventh consecutive day of strikes by hitting Iranian surveillance sites, military logistics infrastructure, underground weapons storage and maritime capabilities.
Iranian media reported strikes early on Saturday in Hormozgan Province on the Strait of Hormuz.
State TV said three people were killed and eight wounded while two bridges and a road tunnel were damaged.
Trump has threatened to launch broad-based air strikes on Iran's infrastructure and has also declined to rule out a ground assault on Iran's coast or islands.
US officials have said attacks on southern Iran are designed in part to give Trump options.
Such moves risk provoking Iran to mount further attacks on the vital infrastructure of Gulf states, or renewed efforts by Tehran's allies in Yemen to disrupt global energy supplies by targeting Red Sea shipping.
