Three crew members have been killed in a Houthi missile strike on a cargo ship off southern Yemen, its owners and the US say - the first deaths caused by the group's attacks on merchant vessels.

The Barbados-flagged True Confidence was abandoned after Wednesday's attack, which inflicted significant damage.

Two of the sailors who died were Filipinos and the other was Vietnamese.

The Houthis say their attacks are in support of the Palestinians in the war between Israel and Hamas in Gaza.

A military spokesman for the Iran-backed group claimed it targeted True Confidence because it was "American" - something the owners denied.

The US military's Central Command (Centcom) condemned the Houthis' "reckless attacks", which it said had "disrupted global trade and taken the lives of international seafarers".

Hours after the attack, US forces conducted strikes on two unmanned aerial vehicles (UAVs) in Yemen, which Centcom said presented an imminent threat to US Navy ships in the region. Houthi-run Al Masirah TV reported that two strikes targeted the airport in the Red Sea city of Hudaydah.

The attack on True Confidence occurred around 12:30 (09:30 GMT) on Wednesday, when the bulk carrier was in the Gulf of Aden, about 50 nautical miles (93km) south-west of the city of Aden, according to its owners.

The vessel was manned by a crew of 20, comprising one Indian, four Vietnamese and 15 Filipino nationals. Three armed guards - two from Sri Lanka and one from Nepal - were also on board.

A Centcom statement said the 183m-long bulk carrier was hit by an anti-ship ballistic missile launched from a Houthi-controlled area of Yemen.

It published an aerial photograph showing significant damage to the bridge and accommodation at the stern of the stricken vessel, on the port side.

Nearby vessels then reported a loud bang and a large plume of smoke.

The Indian Navy's spokesperson said INS Kolkata, a destroyer deployed in the region as part of a US-led naval taskforce, arrived at the scene on Wednesday afternoon and rescued 21 crew members using a helicopter and boats.

Indian sailors provided critical medical aid to the injured and evacuated them to Djibouti on Wednesday evening, the spokesperson added.

A video posted online by the navy showed a fire on board True Confidence and several of its crew members being winched onto helicopters from life rafts.

On Thursday morning, a spokesperson for True Confidence's owner and managers put out a statement confirming that one Vietnamese and two Filipino crew members were killed

Another two Filipino crew members had suffered serious injuries and were being treated at a hospital in Djibouti, it said.

"Owners and managers offer their heartfelt sympathy and condolences to the families of those who have lost their loved ones in this tragic attack and wish for a speedy and full recovery of those who are in hospital."

The statement said True Confidence was currently "drifting well away from land" and that salvage arrangements were being made.

It had been sailing from China to the Red Sea ports of Jeddah in Saudi Arabia and Aqaba in Jordan with a cargo of steel products and trucks.

The statement also said the vessel was owned by True Confidence Shipping SA, which is registered to an address in Liberia, and operated by Third January Maritime Ltd in Greece.

"There is no current connection with any US entity," it added.

Maritime data provider Lloyd's List Intelligence said True Confidence had links to by US-based Oaktree Capital Management before 24 February.

It quoted Oaktree as saying it no longer had any association with the vessel, but that the change of ownership "had not been updated in several shipping databases and is thought to have been used by the Houthis as part of its targeting criteria".

Houthi military spokesman Yahya Sarea said on Wednesday night that its forces had targeted "the American ship True Confidence" after the crew "rejected warning messages from the Yemeni naval forces".

"The Yemeni armed forces persist in upholding their religious, moral and humanitarian duties in supporting the oppressed Palestinian people, and their operations in the Red and Arab Seas will not stop until the aggression stops and the siege on the Palestinian people in the Gaza Strip is lifted," he added.

The US State Department said Washington would continue to hold the Houthis accountable and called on governments around the world to do the same.

"The Houthis have continued to launch these reckless attacks with no regard for the well-being of innocent civilians who are transiting through the Red Sea and now they have unfortunately and tragically killed innocent civilians," spokesman Matthew Miller told reporters.

UK Foreign Secretary Lord Cameron said he was "appalled to hear about the deaths" and condemned the Houthis' "reckless and indiscriminate attacks"

"We will continue to stand up for freedom of navigation and back our words with actions."

After nearly four months of sustained drone and missile attacks by the Houthis against shipping passing through the Gulf of Aden and Red Sea a fatal attack was perhaps, as the British Embassy stated, inevitable.

The US-led naval taskforce has been shooting down as many of these missiles and drones as it can but there are simply too many for them to destroy every single one.

The Houthis seem to have an inexhaustible supply of them. This calls into question the efficacy of the US-led campaign of air strikes that has been targeting Houthi launch sites, ammo depots and Command and Control posts.

Now that the Houthi attacks have turned deadly there are bound to be calls to step up retaliation against them, expanding the range of targets inside Yemen. But this in turn risks escalation in a region already tense due to the humanitarian situation in Gaza.

On Tuesday, US forces shot down a ballistic missile and three UAVs launched from Yemen at the destroyer USS Carney. They also destroyed three anti-ship missiles and three unmanned surface vessels (USVS), or sea drones, in later strikes.

Meanwhile, on Monday the Indian Navy helped put out a fire on board the container ship MSC Sky II, which its operator said had been hit by a missile.

On Sunday, a Belize-flagged cargo ship, Rubymar, sank in the Red Sea two weeks after hit by missiles fired by Houthis. It was the first ship to have been sunk since the Houthi attacks began in November.

The Rubymar was near the Bab al-Mandab Strait, which connects the Gulf of Aden with the Red Sea, when it was attacked. The crew was rescued and the vessel began slowly taking on water.

It was carrying a cargo of 21,000 metric tonnes of ammonium nitrate fertiliser, which the US military said presented an environmental risk in the Red Sea.

Additional reporting by David Gritten