The bodies of three crew members have been recovered from the Atlantic after a supply vessel operated by a French oil services group sank in hurricane conditions, bringing the death toll to four, according to a Martinique government official.

The Luxembourg-flagged Bourbon Rhode, crewed mainly by Ukrainians, ran into difficulty some 1,200 nautical miles from the French Caribbean island of Martinique last Thursday as it sailed into hurricane Lorenzo, and was later confirmed to have sunk.

A major search operation was launched for the 14 people on board the tug supply vessel. Three crew members who had made their way onto a lifeboat were rescued on Saturday.

One was found dead shortly afterwards, and another three on Monday and Tuesday, Martinique governor Franck Robine said late Tuesday.

The Bourbon Rhode's operator, French marine logistics group Bourbon, which provides services to oil rigs, said the search was continuing for the seven missing crew members.

Three Bourbon Rhode crew members were rescued from a lifebaot
Three Bourbon Rhode crew members were rescued from a lifebaot AFP / HO

The ship passed near the eye of Lorenzo, a category 4 hurricane that produced waves as high as 10 metres (30 feet), according to the survivors.

"The chances of survival, even for someone with a wetsuit and life jacket, are extremely low," Robine said.

The search area stretches over 130 by 130 nautical miles in the middle of the Atlantic.

Bourbon has chartered a ship to take part in the search, and military planes were flying over the area several times a day.

Twelve commercial vessels have been mobilised in the search, and all other ships in the area have been asked to be on the lookout.