The U.S. Coast Guard says its search continues for 31 Cubans reported missing after their smuggling boat overturned and sank in the Florida Straits.

The Coast Guard began its search after three Cubans, rescued by a merchant ship late Sunday, said their boat had overturned on August 16, about 15 minutes into a trip to Florida from Cuba. The three said they were the only ones aboard wearing life vests. They were returned to Cuba.

The Coast Guard found a capsized boat Monday about 26 kilometers from where the merchant vessel rescued the three Cubans. There were no bodies or survivors found near the boat.

A Coast Guardsman said the number of people reportedly in the boat indicated that they were likely trying to enter the United States illegally.

Some information for this report provided by AP and Reuters.