Kuwait, which hosts a US base, said it had intercepted "hostile missile and drone threats", but did not confirm the target.
It is the second time in three days that the US has attacked targets in Iran - saying they were conducted in self-defence. The renewed hostilities threaten a fragile ceasefire between Washington and Tehran.
The IRGC said the attack on the US air base took place in the early hours of Thursday morning and targeted "the source" of earlier US strikes on Iran, according to state broadcaster IRIB.
US Central Command (Centcom) said Iran's attack on Kuwait was an "egregious ceasefire violation" that occurred "hours after Iranian forces launched five one-way attack drones that posed a clear threat in and near the Strait of Hormuz".
