LONDON/WASHINGTON/DAVOS, Switzerland, Jan 17 (Reuters) - The U.S. on Wednesday returned the Yemen-based Houthi rebels to a list of terrorist groups, as the militants claimed their second attack this week on a U.S. operated vessel in the Red Sea region.

Attacks by the Iran-allied Houthi militia on ships in the region since November have slowed trade between Asia and Europe and alarmed major powers - an escalation of the more than three-month-old war between Israel and Palestinian Hamas militants in Gaza.

The Houthis say they are acting in solidarity with Palestinians and have threatened to expand attacks to include U.S. ships in response to the American and British strikes.

In a sign it remains undeterred, the Houthi movement on Wednesday said it made a "direct hit" with missiles on the U.S. Genco Picardy bulk carrier.

The attack, which marked the second on a U.S.-linked vessel in the area this week, was confirmed by U.S. shipping operator Genco, which said its vessel was hit by a projectile while it transited the Gulf of Aden with a cargo of phosphate rock.

Genco said there were no injuries to crew and the ship suffered limited damage to its gangway and was on a course out of the area.

"The naval forces will not hesitate to target all sources of threat in the Red and Arabian sea within the legitimate right to defend Yemen and to continue supporting the oppressed Palestinian people," the group's military spokesperson Yahya Sarea said in a statement.

On Monday, Houthi forces struck the U.S.-owned and operated dry bulk ship Gibraltar Eagle with an anti-ship ballistic missile. There were no reports of injuries or significant damage.

U.S. officials said the "Specially Designated Global Terrorist" listing was aimed at cutting off funding and weapons the Houthis have used to attack or hijack ships.

A Houthi spokesman told Reuters that attacks on ships heading to Israel would continue and the designation would not affect its position.

Iranian Foreign Minister Hossein Amirabdollahian, whose country backs Hamas in its war with Israel, said an end to the war in Gaza was needed to remove the threat to shipping.

"The security of the Red Sea is tied to the developments in Gaza, and everyone will suffer if Israel's crimes in Gaza do not stop ... All the (resistance) fronts will remain active," Amirabdollahian said at the World Economic Forum in Davos.