The Coast Guard searched the Florida Straits on Monday after three Cubans rescued at sea said they had been aboard a speed boat that sank with 31 others on board.

Coast Guard crews located a capsized boat matching the Cubans' description about 16 miles from where the three were picked up, but they did not find any bodies trapped under it when they righted it.

The three, who were wearing flotation devices, were rescued after five days in the water Sunday by a merchant ship about 30 miles north of Matanzas, Cuba, and taken back to an unspecified Cuban port. They told officials that they had been on a 28-foot speed boat that sank. The Cuban government notified the Coast Guard, which began searching with ships and helicopters late Sunday.

The Coast Guard was still trying to contact the survivors to get more details, spokesman Luis Diaz said.

If the report is accurate and the others died, it would be the deadliest known migrant boat trip from Cuba to Florida in recent years, he said.

No Cuban Americans had come forward Monday to report that they were expecting relatives to make the trip, Coast Guard officials said.

U.S. officials do not know where the boat was headed, but "34 people in one boat is usually an indication that they were trying to enter the United States illegally," Coast Guard Petty Officer Ryan Doss said. A speed boat that size should not have been carrying more than 10 people, he said.

Cuba sent a boat and an aircraft to help with the search, and a British navy ship that was in the area joined the effort for a time Monday, Coast Guard officials said.

Thousands of migrants from Cuba and other Caribbean nations try to reach the United States illegally by boat each year. U.S. officials say they do not know how many die trying.

Cubans who reach U.S. soil generally are allowed to stay under the "wet foot, dry foot" policy, but those caught at sea are usually returned home. Many have tried to reach the United States aboard Florida-based speed boats run by smugglers hired illicitly by U.S. relatives.

The deadliest migrant trip occurred three years ago when more than 20 migrants were believed to have died trying to reach Florida on a 24-foot boat, Diaz said.