US forces said they destroyed an underwater drone and nearly 20 ballistic missiles in a series of strikes against Yemen's Huthi rebels, who threatened on Tuesday to step up their attacks in the Red Sea during Ramadan.

The US Central Command (CENTCOM) said in a statement Monday night that the strikes were carried out after the Huthis fired two missiles towards a Singaporean-owned, Liberian-flagged merchant ship called the Pinocchio.

"The missiles did not impact the vessel and there were no injuries or damage reported," CENTCOM said. 

Hours later, it added, US forces "conducted six self-defence strikes destroying an unmanned underwater vessel and 18 anti-ship missiles in Houthi controlled areas of Yemen".

The Huthis claimed responsibility for the attack on the Pinocchio in a statement early Tuesday, maintaining the missile strike "was accurate".

The British maritime security agency UKMTO had previously said a ship in the area "reported a sound of an explosion" in its vicinity southwest of the Yemeni port of Salif, and that US-led coalition forces were investigating.

The Huthi statement went on to say that "military operations will be escalated... during the month of Ramadan".

The attacks would be "in support of the oppressed Palestinian people" and those in the Gaza Strip, the Huthi's military spokesman Yahya Saree said.

Since November, the Iran-backed Huthis, who control the capital Sanaa, have been attacking ships in the Red Sea, in professed solidarity with Palestinians during the Israel's war against Hamas militants in Gaza.

The attacks have sent insurance costs spiralling for vessels plying the key trade route and prompted many shipping firms to take the far longer passage around the southern tip of Africa instead.

Since January, the United States and Britain have launched repeated strikes on Huthi targets in Yemen in response to the attacks, but the actions have not deterred the rebels.