Three projectiles hit a merchant vessel off Yemen's rebel-held port city of Hodeida on Wednesday, causing a fire onboard and leaving the ship without engine power, a British maritime security agency said.

Authorities in Athens identified the vessel as the Greek-flagged Sounion oil tanker, and Greece's Maritime Affairs Minister Christos Stylianides condemned "a serious threat" to international shipping.

The tanker was "struck by two unidentified projectiles before being hit by a third", said the United Kingdom Maritime Trade Operations (UKMTO), which is run by Britain's Royal Navy.

Its crew earlier exchanged fire with two small vessels, one with three to five people onboard while the second carried around 10, said the agency.

"There is a fire onboard and the vessel has lost engine power," UKMTO said, adding that "the vessel is drifting and not under command".

Both the UKMTO and the Greek port authority said there were no reports of casualties.

A spokesperson for the port authority said the Sounion, an oil products tanker owned by Greek shipping company Delta Tankers, carried a crew of 25 people, mostly Filipinos.

It had departed from Iraq and was destined for a port near Athens where many refineries are based, the Greek port authority said. It said the ship could have been hit either by missiles or drones.

There was no immediate claim of responsibility but the attack came as the Iran-backed Huthi rebels keep up a nine-month-old campaign against international shipping in the Red Sea and the Gulf of Aden that they say is in support of Gaza.

Stylianides in a statement "condemned the attack, which constitutes a flagrant violation of international law and a serious threat to the security of international shipping".

"Such acts put the lives of seafarers at risk and disrupt the free movement of goods along vital maritime routes," the minister added.

In a separate incident south of the Yemeni port city of Aden on Wednesday, another ship reported three explosions in the water in close proximity, UKMTO said.

The crew are reported safe and vessel is proceeding to the next port of call, the agency added. The Huthis' campaign of rocket and drone attacks has severely disrupted maritime traffic through the Red Sea, which normally accounts for up to 12 percent of world trade.

Many merchant vessels passing through the Red Sea now have security teams on board. The United States and Britain have responded to the attacks by striking Huthi targets in Yemen since January, but it has done little to deter the rebels.