A US Navy warship shot down a missile Friday that was fired at it by Yemen's Iran-backed Huthi rebels, who have carried out two months of attacks on international shipping, the military said.

US and British forces carried out two rounds of joint strikes aimed at reducing the Huthis' ability to target vessels transiting a key maritime trade route and Washington has also launched a series of unilateral air raids, but the Huthis have vowed to continue their attacks.

"Iranian-backed Huthi militants fired one anti-ship ballistic missile from Huthi-controlled areas of Yemen toward Arleigh-Burke class destroyer USS Carney (DDG 64) in the Gulf of Aden," the US Central Command (CENTCOM) said in a statement on social media.

"The missile was successfully shot down by USS Carney. There were no injuries or damage reported," CENTCOM said.

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

The Yemeni rebels have since declared US and British interests to be legitimate targets as well.

In addition to military action, Washington is seeking to put diplomatic and financial pressure on the Huthis, redesignating them as a terrorist organization last week after previously having dropped that label soon after President Joe Biden took office.