American forces shot down three drones and a missile fired toward a destroyer in the Red Sea on Tuesday, the US military said, after Yemen's Houthis announced they had targeted two of Washington's warships.

The Iran-backed Houthis have been attacking shipping in the Red Sea for months, and repeated American and British strikes have so far failed to prevent them from threatening the vital trade route.

"US Central Command (CENTCOM) forces shot down one anti-ship ballistic missile and three one-way attack unmanned aerial systems launched from Iranian-backed Houthi controlled areas of Yemen toward USS Carney (DDG 64) in the Red Sea," the military command said in a statement.

"There are no injuries or damage to the ship," CENTCOM said, adding that American forces later destroyed three anti-ship missiles and three naval drones in Houthi-controlled areas of Yemen.

Houthi military spokesman Yahya Saree said earlier in the day that their forces had targeted two US destroyers in the Red Sea "with a number of naval missiles and drones."

The Houthis "will not stop until the aggression stops and the siege imposed on the Palestinian people in the Gaza Strip is lifted," Saree said on social media.

They began attacking Red Sea shipping in November, saying they were hitting Israel-linked vessels in support of Palestinians in Gaza, which has been ravaged by the Israel-Hamas war.

US and UK forces responded with strikes against the Houthis, who have since declared American and British interests to be legitimate targets as well.

Anger over Israel's devastating campaign in Gaza -- which began after an unprecedented Hamas attack on October 7 -- has grown across the Middle East, stoking violence involving Iran-backed groups in Lebanon, Iraq, Syria and Yemen.