Survivors who were rescued today near the British Virgin Islands told officials that 13 Cubans, a Colombian and a Dominican were missing.
They said the boat set off from the Dutch island of St Maarten on July 9 and was headed for the US territory, where Cubans have legal right to remain if they can reach land.
British and Dutch rescuers also participated in the search.
Some Cuban migrants have tried to use other Caribbean islands as stepping stones to reach the US Virgin Islands rather than taking the more common sea journey directly from the island to Florida, Mexico or Central America.