Rescue efforts are winding down after the sinking of a Bourbon Offshore vessel in the mid-Atlantic, as the French vessel owner has found only three survivors with seven other crew members still missing after almost two weeks of searching.

Operations have been carried out since 26 September and the bodies of four seafarers have been recovered.

The company said on Monday afternoon that the three survivors have now arrived at the Martinique port of Fort de France on board the French Navy vessel Ventose.

"The three seafarers, in good health, have been taken care of by the health structures and have already been reunited with their families," it said.

Bourbon said it will now work “to understand” the circumstances of the sinking of its vessel Bourbon Rhode, which had 14 crew on board.

The vessel sank after it was caught up in Hurricane Lorenzo. Bourbon Rhode was en route to Guyana.

Search operations were carried out by French authorities with the support of the US authorities, Bourbon said.

However, after four days of search with no results, the search operations will be scaled down.

“Several vessels have continued to survey the search area today, with no results for the past 4 days. The (Regional Operational Centre for Surveillance and Rescue) CROSS has decided to make the search operation evolve,” Bourbon said.

“It will regularly disseminate messages to vessels in the shipwreck zone and ask them to carry out adapted watch,” the company said.

“We are working in close co-operation with the various stakeholders to understand the facts and circumstances of this tragedy,” chief executive Gael Bodenes added.

Bourbon clarified later on Monday: "The Alp Striker vessel ... is still surveying the area to find the missing seafarers and all merchant vessels operating in this area are mobilized to set up an appropriate watch."

Bodenes said: "We thank the entire maritime community for its many signs of solidarity, so precious in these difficult times. I would like to reiterate our heartfelt thanks to the CROSS teams, the crews of the French Navy and the commercial vessels involved in search operations."

The families of the crew members have launched petitions online urging authorities to continue the search for the seven missing crew, mostly Ukrainians and Croats.

The petition had over 30,000 signatures a day after it was launched.