A missile strike damaged a merchant ship in the Red Sea off Yemen, marine security monitors said Friday, as the country's Iran-backed Huthi rebels threatened to expand their months-long harassment campaign which has disrupted global trade.

The crew was not injured and the vessel continued its journey, said the British navy's United Kingdom Marine Trade Operations, and security firm Ambrey, after the incident west of the rebel-held port of Hodeida in the early hours of Friday.

"A merchant vessel has reported that they have been struck by a missile and the vessel has sustained some damage," said UKMTO.

There was no immediate claim of responsibility from the Huthis, who have launched dozens of missile and drone strikes on shipping in the commercially vital seaway over the past four months.

The rebels say they are targeting Israel-linked shipping as part of an "axis of resistance" of Iran allies and proxies, in protest at Israel's war against Hamas in the Gaza Strip.

The Huthi attacks, including a deadly assault on a bulk carrier last week and the sinking of a ship carrying thousands of tonnes of fertiliser, have triggered reprisal strikes by US and British forces.

On Thursday, the US military said it had destroyed nine anti-ship ballistic missiles and two drones after the Huthis fired on ships in the Red Sea and Gulf of Aden.

Such exchanges have become a frequent occurrence in the area, sending shipping insurance costs soaring and prompting many firms to detour around the southern tip of Africa.

Late on Thursday, rebel leader Abdul Malik al-Huthi said the Huthis would expand their attacks to ships taking the longer route around Africa's Cape of Good Hope.

"We are moving, with the grace and help of God Almighty, to prevent them from crossing even through the Indian Ocean and from South Africa," he said in a speech broadcast by the rebels' Al-Masirah TV channel.

"We have begun implementing our related operations," he added.

Twelve "targeting operations" using 58 missiles were carried out against commercial and military ships this week in the Red Sea, Gulf of Aden and the Arabian Sea, the Huthi leader said.