The Iran-backed Huthis have been targeting merchant vessels transiting the vital Red Sea trade route for months but Wednesday's deaths were the first reported fatalities resulting from such an attack.

An anti-ship ballistic missile struck the Barbados-flagged, Liberian-owned M/V True Confidence, after which its crew reported "three fatalities, at least four injuries, of which three are in critical condition, and significant damage to the ship", the US Central Command (CENTCOM) said in a statement.

"The crew abandoned the ship and coalition warships responded and are assessing the situation," it said, noting the attack was the fifth time the Huthis had launched an anti-ship ballistic missile in two days.

"These reckless attacks by the Huthis have disrupted global trade and taken the lives of international seafarers," CENTCOM said.

The Indian Navy said, in a post on social media platform X, that it rescued 21 crew members, including an Indian national.

It published video footage of the rescue operation, saying eight people were winched to safety by helicopter while others were evacuated to hospitals in Dijbouti.

The Philippine government's Department of Migrant Workers said in a statement on Thursday that two of the crew members killed were Filipinos and two others were "severely injured".

Huthi military spokesman Yahya Saree wrote on social media that the True Confidence was targeted with multiple missiles "after the ship's crew rejected warning messages" from the Huthis.

- US military strikes -

CENTCOM said several hours after the True Confidence was hit that it had carried out strikes against "two unmanned aerial vehicles in a Huthi-controlled area of Yemen that presented an imminent threat to merchant vessels and US Navy ships".

"These actions are taken to protect freedom of navigation and make international waters safer and more secure for US Navy and merchant vessels," it said in a separate statement without elaborating.

The United States and Britain have launched repeated strikes on Huthi targets in Yemen since January in response to the ship attacks but the rebels have continued to target merchant vessels.

The British embassy in Sanaa said earlier the death toll on board the True Confidence was at least two, describing the loss of life as "the sad but inevitable consequence of the Huthis recklessly firing missiles at international shipping".

British Foreign Secretary David Cameron promised that "we will continue to stand up for freedom of navigation and back our words with actions".

The Huthis began attacking ships in the Gulf of Aden and the Red Sea in November, a campaign they say is intended to signal solidarity with Palestinians in Gaza.

They have vowed to strike Israeli, British and American ships, as well as vessels heading to Israeli ports, disrupting traffic through the vital trade route off Yemen's shores.

The latest incident comes after a Belize-flagged, Lebanese-operated ship sank on Saturday with 21,000 metric tonnes of ammonium phosphate sulfate fertiliser on board.

The ship, called the Rubymar, had been taking on water since it was hit by a Huthi missile on February 18 that damaged its hull and forced the evacuation of its crew to Djibouti.

The flurry of Huthi strikes has caused several major shipping firms to suspend passage through the Red Sea, which usually carries around 12 percent of global trade.