The US Coast Guard ship leaves the coast guard base in Miami Beach, Florida. AP

Rescue crews searched late into the night on Tuesday for 39 people reported missing in the Atlantic off Florida by a man found clinging to a boat that capsized in what the US Coast Guard called a suspected human smuggling attempt gone awry.

The survivor told authorities that he had left the Bahamas' Bimini islands, about 50 miles (80 km) east of Miami, in a boat with 39 other people on Saturday night, the Coast Guard said in a statement posted online.

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A good Samaritan called the Coast Guard early Tuesday after rescuing a man clinging to the boat 45 miles (72 kilometers) east of Fort Pierce, the maritime security agency reported on Twitter.

The man said he was with a group of 39 others that left the island of Bimini in the Bahamas on Saturday night. He said the boat capsized in severe weather and that no one was wearing life jackets.

This handout image shows a capsized vessel approximately 45 miles east of Fort Pierce inlet, Florida. AFP

The survivor was brought to a hospital for symptoms of dehydration and sun exposure.

According to the survivor, the group's vessel capsized on Sunday morning when it hit rough weather about 45 miles (72.4 km) east of Fort Pierce Inlet, off Florida's Atlantic coast about midway between Miami and Cape Canaveral, but no one was wearing a life jacket, the Coast Guard said.

The accident coincided with a small-craft advisory posted in that area, with steady winds clocked at up to 23 miles (37 km) per hour and 9-foot (3-meter) seas, according to the Coast Guard.

It added later that air and surface crews would "continue to search throughout the night" for the missing people.

An image released by the Coast Guard showed the capsized vessel in the water with a man straddling the hull.

The survivor was taken to a hospital to be treated for dehydration and sun exposure, the Coast Guard said.

The survivor was taken to hospital for treatment of dehydration and sun exposure.

Through Tuesday, Coast Guard cutter crews, helicopter teams, search planes and a US Navy air crew criss-crossed an area spanning more than 1,300 square miles (3,367 square km), about the size of Rhode Island, between Bimini and Fort Pierce Inlet, the statement said.

US authorities noted an increase in migration from Cuba by sea in recent months. In July, the country saw scores of demonstrations triggered by economic strife, medical and food shortages and anger at the government.