Yemen's Huthi rebels launched six missiles toward two merchant ships on Tuesday, reportedly causing light damage to one of the vessels, the US military said.

The launches came three days after US and UK forces launched a wave of air raids against the Iran-backed Huthis -- their third round of joint military action in response to the rebels' persistent attacks on shipping.

"Iranian-backed Huthi militants fired six anti-ship ballistic missiles (ASBM) from Huthi-controlled areas of Yemen toward the Southern Red Sea and the Gulf of Aden", US Central Command (CENTCOM) said in a statement.

Three of the missiles were aimed at the MV Star Nasia, a Marshall Islands-flagged bulk carrier that is Greek owned and operated, the military command said.

"MV Star Nasia reported an explosion near the ship causing minor damage but no injuries", while a second missile later landed nearby and a third was shot down by a US destroyer, CENTCOM said.

The other three missiles were apparently aimed at the MV Morning Tide, a Barbados-flagged, UK-owned cargo ship, but they exploded in the Red Sea without causing damage.

The Huthis had earlier said they struck US and British ships in two Red Sea attacks -- the latest among dozens of incidents that have disrupted global shipping.

The Iran-backed rebels, who control much of the war-torn country, have been harassing shipping in a campaign they say is in solidarity with Palestinians in the Israel-Hamas war.

Huthi spokesman Yahya Saree said the first attack on Tuesday "targeted the American ship Star Nasia, while the other targeted the British ship Morning Tide".

- Trade disruption -

The Huthis "will carry out more military operations against all hostile American-British targets" in self-defence, Saree warned on X, formerly Twitter.

The Greek merchant marine ministry said the Star Nasia sustained material damage but the hull did not appear to have been breached and no injuries were reported among the Filipino crew.

The Huthis have either attacked or threatened commercial vessels more than 40 times since November 19, according to the Pentagon.

In a helicopter assault that day, the Huthis captured the Galaxy Leader, an Israel-linked cargo vessel, and its 25 international crew members, who include at least two Bulgarian nationals.

They forced it to the Hodeidah port, where it has remained.

Bulgarian Transport Minister Georgy Gvozdeykov said Tuesday that the sailors of the Galaxy Leader were "safe and sound" and would shortly return to Bulgaria.

"The information we have... on the sailors of the Galaxy Leader captured in the Red Sea is that they are well, safe and sound and are staying in a hotel," the minister told private Bulgarian television station bTV.

The Huthi attacks have prompted some shipping companies to detour around southern Africa to avoid the Red Sea, a vital route that normally carries about 12 percent of global maritime trade.

Most trade between Asia and Europe usually passes through the Red Sea and the Suez Canal that leads to the Mediterranean Sea.

According to the International Monetary Fund's PortWatch platform, total transit volume through the Suez Canal was down 37 percent this year by January 16 compared with the same period a year earlier.