The United States launched new airstrikes Saturday to "punish" Iran after reporting the first US military deaths since renewing its hostilities with the Islamic republic.

Iran's supreme leader vowed to teach the Americans "unforgettable lessons" as it struck infrastructure around the Gulf in retaliation for a week of intensifying US attacks, which Iran said had hit an airport, a railway station and bridges.

A month after the foes signed a now-abandoned preliminary deal aimed at ending their war, Iran hit an oil facility in Kuwait as well as a power and water plant, authorities in the Gulf state said, while in Bahrain the army said air defences repelled a wave of Iranian attacks.

Tehran 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.

That brought to 16 the confirmed number of US military fatalities since the conflict began on February 28.