The US embassy later said on Wednesday that Houthis kidnapped mariners from the ship they attacked.

The Eternity C, a Liberian-flagged bulk carrier, was badly damaged in the attack that started on Monday and continued into Tuesday, before the ship sank.

Yemen's rebels claimed responsibility for the attack, which came a day after they boarded and sank the Magic Seas - their first attack on shipping this year.

Their resumed attacks mark the end of a months-long lull and threaten a May ceasefire with the United States that ended weeks of strikes on Houthi targets.

"The naval force of the Yemeni Armed Forces targeted the ship Eternity C," Houthi military spokesman Yahya Saree said, claiming that the vessel was headed for the Israeli port of Eilat and was attacked in support of Palestinians in Gaza.

Saree said the Houthis had "moved to rescue a number of the ship's crew, provide them with medical care, and transport them to a safe location".

The attack was carried out with an unmanned vessel and six cruise and ballistic missiles, Saree added.

Operation Aspides - the EU naval task force in the Red Sea - told AFP that five Filipinos and one Indian had been rescued, while 19 others were still missing.

Rescue and search operations are ongoing, it said.

The UN envoy for Yemen, Hans Grundberg, expressed "grave concern" over attacks that resulted in "civilian loss of life and casualties as well as the potential for environmental damage".

"Yemen must not be drawn deeper into regional crises that threaten to unravel the already extremely fragile situation in the country," he said.

A total of 25 people were aboard the Eternity, the EU task force said. The Philippine authorities said 21 were citizens.

On Tuesday, Aspides said three people were killed in the attack on the Eternity C and at least two were injured - including a Russian electrician who lost a leg.

Saree warned "all companies dealing with the ports of occupied Palestine (Israel) that their ships and crews will be targeted" until Israel has been forced to "lift the siege on our brothers in Gaza, cease the aggression against them and end the ongoing war".

The Houthis began their attacks on Red Sea shipping in late 2023, saying they were in support of Palestinians in Gaza.

On Monday, they said they hit the Magic Seas because its owner had done business with Israel and used its ports.

The rebels released a video showing masked gunmen storming the Magic Seas and simultaneous explosions that scuttled the bulk carrier.

Both ships had likely been attacked "due to prior Israeli port calls or ownership/ship manager affiliations", according to the Joint Maritime Information Centre, run by Western navies.

Huthi attacks have prompted many shipping firms to make the time-consuming detour around the southern tip of Africa to avoid the Red Sea, which normally carries about 12 per cent of global trade.

The Houthis had threatened to renew their attacks after the Gaza ceasefire collapsed in March, prompting a deadly US bombing campaign against the rebels that ended with a May ceasefire.

However, the rebels said they would continue to target "Israeli ships".

In a statement on Tuesday, the US embassy in Yemen blamed the Huthis for the Eternity C attack, calling it "the most violent" yet and accusing them of "undermining freedom of navigation in the Red Sea".

Israel, which has also come under direct missile and drone attack by the Houthis, has carried out multiple strikes on rebel targets in Yemen, most recently on Sunday.