Iran's Revolutionary Guards said earlier on Thursday that its forces had targeted a US airbase.
US Central Command said on Thursday that Iran had launched a ballistic missile towards Kuwait.
In a statement posted on X, CENTCOM said Kuwaiti forces successfully intercepted the missile but called it an "egregious ceasefire violation by the Iranian regime".
Washington and Tehran had agreed to a ceasefire in April, but the two nations have traded a series of strikes this week amid mounting pressure to secure a deal to end the conflict.
Iran's Revolutionary Guards said earlier in the day that its forces had targeted a US airbase in retaliation for American strikes near an airport in the south of the country, the semi-official Tasnim News Agency reported.
"Following the pre-dawn aggression today by the invading American army against a point on the outskirts of Bandar Abbas Airport using aerial projectiles, the American airbase, as the origin of the aggression, was targeted at 4:50 a.m.," the IRGC said in a statement.
It added that it was a "serious warning" to Washington and that any further US aggression would be met with a "more decisive" response.
While the Guards did not specify which base had been targeted, Kuwait's military had said on Thursday that it was responding to "hostile missile and drone attacks."
It comes after the US said it had carried out a series of "defensive strikes" against Iran, shooting down four one-way attack drones in the Strait of Hormuz and a ground control station in Bandar Abbas.
It marked the second such US strikes in three days.