The death toll from the sinking late last week of a Bourbon Offshore vessel that was en route to Guyana has hit four, with the search continuing for seven missing crew members.

The body of another of the 14 original crew members of the Bourbon Rhode has been recovered from the water after the vessel sank in the mid-Atlantic after it was caught up in Hurricane Lorenzo.

The body of the latest confirmed casualty has been taken to the French Navy frigate Ventose, owner Bourbon said.

On Monday, one person was confirmed to have died, while two more bodies were recovered on Tuesday.

Three crew members were rescued from a lifeboat on Saturday, two days after the anchor-handler started to take in water as it was caught in the eye of the hurricane, which was a category four system.

"On behalf of Bourbon, I would like to express our condolences to the family and friends of the deceased seafarer. We are at their side to accompany them through this terrible ordeal," Bourbon crisis cell director Cyrille Le Bris said on Wednesday.

"Despite significant search resources for the rescue of the crew, the fate of the missing is an ever-increasing source of anxiety for the families.

"We remain fully mobilised to pursue relief operations and reiterate our warm thanks to all the teams that have volunteered and are helping us in our search."

The vessel was in transit 1200 nautical miles off Martinique island and 60 nautical miles south-south east from the eye of Hurricane Lorenzo.

Vessel-tracking data shows that it was headed to Guyana's capital, Georgetown.