The Iran-backed Houthi rebels of Yemen have stepped up attacks in the Red Sea, one of the world's busiest shipping routes, and are determined to keep hitting ships until the Israeli war in Gaza stops.

The Houthis said their attacks are in response to “Israeli aggression on Gaza”, where more than 18,800 people have been killed, including 8,000 children and 6,200 women.

Washington sent missile destroyer USS The Sullivans to join the 19 warships it has around the Mediterranean.

"The Sullivans presence demonstrates our commitment, flexibility and capability to operate throughout the region," according the US Sixth Fleet.

US National Security Adviser Jake Sullivan spent several days in the region and said that Washington was prepared to take steps against the Houthis.

France's Foreign Minister said Houthi attacks “cannot go unanswered”.

“We are studying several solutions,” Catherine Colonna said during a trip to Israel on Sunday, including, a “defensive role” to keep such attacks from happening.

On Saturday, the rebels launched a wave of 14 one-way attack drones, all of which were “shot down with no damage to ships in the area or reported injuries”, the US military's Central Command claimed.

This happened a day after a drone attack on the Liberian-flagged MSC Palatium III, for which the Houthis claimed responsibility.

No injuries were reported in the attack on the vessel, which suffered some damage and was taken out of service, MSC said. Another Liberian-flagged vessel, Hapag Lloyd's Al Jasrah, was hit by a missile, the US military said.

The Irish-owned Ardmore Encounter chemical tanker was struck on December 13 while in transit from India.

Ardmore Shipping reported the crew escaped unharmed, and that no one boarded the vessel, although the UK Maritime Trade Operations (UKMTO) said the vessel took fire from “three armed individuals in a small boat” 50 nautical miles off the Yemeni port of Hodeidah.

On December 11, the Houthis claimed to attack the Norwegian commercial tanker Strinda as it was delivering crude oil to an Israeli terminal, Houthi military official Yahya Saree said.

Last month, the USS Mason responded to a distress call in the Gulf of Aden from the Central Park vessel which was carrying phosphoric acid as it was seized by militants.

The vessel was safe, US officials said at the time.

One of the ships targeted on November 19, the Bahamas-flagged Galaxy Leader, was converted to a tourism attraction for Yemenis.

There have been at least 13 Houthi attacks on ships in the Red Sea that have either hit or were near misses since November.

The conflict has also caused major disruption to the Red Sea shipping lane between Asia and Europe, with two more companies announcing they were redirecting their vessels following repeated attacks by Yemeni rebels allied with Hamas.

About 10 per cent of annual global trade passes through the Red Sea.

Tim Lenderking, US special envoy for Yemen, said that the Houthi attacks could derail peace talks in Yemen.

He said talks in the Gulf over the weekend aimed to “safeguard maritime security in the Red Sea and the Gulf of Aden amid Iranian-enabled Houthi attacks on international shipping threatening almost two years of joint progress in Yemen peace efforts”.