(CNN) -- A 6-year-old Cuban boy drowned Thursday after a smuggler's boat carrying him and 30 other people capsized as a U.S. Coast Guard vessel attempted to intercept it south of Florida, the Coast Guard said.

The boat was spotted on radar about 1 a.m. Thursday about 45 miles south of Key West, according to Lt. Cmdr. Chris O'Neill.

The cutter Dauntless gave chase and drew within sight of the 33-foot "go fast" boat, but the boat sped up pulled away, the Coast Guard said.

"The suspected smuggling boat was moving erratically in an attempt to flee," O'Neill said.

The Coast Guard cutter lost track of the boat, he said. About 20 minutes later, the crew found the boat capsized with about 30 people clinging to the boat or in the water.

After they were rescued they told authorities the 6-year-old boy was missing.

While a Coast Guard helicopter searched the water, the crew of the Dauntless tried to right the boat. When they did so, "the youngster was found inside," O'Neill said.

The migrants are being held at sea aboard the Coast Guard cutter while U.S. officials decide their immigration status, the Coast Guard said.

Under what is called the wet-foot, dry-foot policy, Cubans intercepted at sea are normally returned to Cuba; only those who reach U.S. land are allowed to remain.

However, an Immigration and Customs Enforcement official said asylum officers typically will interview migrants at sea to determine if a migrant's asylum claim needs further investigation. If so, that person would be taken to the U.S. naval base at Guantanamo Bay, Cuba. Any such migrants granted asylum would be resettled in a third country, the official said.

CNN's Jeanne Meserve, Susan Candiotti and Mike Ahlers contributed to this report.