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

The three were rescued Sunday about 30 miles north of Matanzas, Cuba (search), by a merchant ship and taken back to Cuba, where they told officials that they were on a 28-foot boat that sank. The Cuban government notified the U.S. Coast Guard, which began its search with ships and helicopters late Sunday.

The Coast Guard said it found a capsized boat about 16 miles from where the trio were found, but it could not be determined if it was the boat they had been on. No bodies were immediately found.

Petty Officer Ryan Doss said a Coast Guard ship was attempting to raise the boat to see if any bodies or debris were underneath.

It wasn't known where the boat was headed, Doss said, but "34 people in one boat is usually an indication that they were trying to enter the United States illegally,"

The boat should have been carrying 10 people, at most, he said.