Armed Yemeni supporters of Houthis sit on the back of an armoured vehicle during an anti-US rally in Sanaa. File/AFP

Yemen's Houthis fired three missiles at two merchant ships in the Red Sea on Wednesday in their latest attack in the commercially vital waterway, the White House and the Iran-backed rebels said.

It came after the Houthis vowed to keep up their attacks despite repeated US and British strikes against them.

One missile missed its target and a US Navy destroyer shot down the other two, National Security Council spokesman John Kirby said.

The continuing Houthi action "means we're obviously still going to have to do what we have to do to protect that shipping," he added.

US Central Command said the missiles were fired "toward the US-flagged, owned, and operated container ship M/V Maersk Detroit" without mentioning a second vessel being targeted.

No injuries or damage to the ship were reported, CENTCOM added.

Danish shipping giant Maersk earlier said two ships belonging to a US subsidiary and bound for the Red Sea turned back after hearing explosions while transiting the Bab al-Mandeb strait between the Horn of Africa and the Arabian Peninsula.

A US navy escort accompanying the Maersk Detroit and the Maersk Chesapeake also "intercepted multiple projectiles", the company said.

"The crew, ship, and cargo are safe and unharmed. The US Navy has turned both ships around and is escorting them back to the Gulf of Aden," it added.

The Houthis later confirmed a "clash" had taken place with American warships while they were protecting the two US commercial ships.

Their military spokesman Yahya Saree claimed several of the group's missiles hit their targets, forcing the US merchant ships to turn back.

The Houthis, who have been launching attacks on ships since November over Israel’s war on Hamas in the Gaza Strip, later claimed the attacks in a prerecorded statement by their military spokesman, Brig. Gen. Yahya Saree. He vowed the Houthis would continue their attacks.

Since November, the rebels have repeatedly targeted ships in the Red Sea, saying they were avenging Israel’s offensive in Gaza against Hamas. But they have frequently targeted vessels with tenuous or no clear links to Israel, imperiling shipping in a key route for global trade.

Agencies