By Ian Simpson and Laila Kearney

(Reuters) - Searchers have recovered the body of one of the family members whose sailboat went missing off the Florida coast three days ago, a Coast Guard official said on Wednesday.

A Coast Guard search helicopter found the body at about 4:30 p.m. EDT and turned it over to local authorities for positive identification, said Captain Gregory Case, the St. Petersburg sector commander.

"We still have three persons out there that we are trying desperately to locate and we still have hope for that," Case told reporters. He declined to give details about the body.

Ace Kimberly, 45, two sons aged 13 and 15, and a 17-year-old daughter were last seen on Sunday when they set sail from Sarasota, Florida, headed to Fort Myers. They were on the family's 29-foot (9-meter) sailboat.

Case said the vessel ran into a storm with 6-foot (1.8 m)seas on Sunday off Englewood, a community about 30 miles (48 km) south of Sarasota.

The Coast Guard has said the family had lived on the vessel for about a year. They were traveling to Fort Myers for repairs to the boat, which was in poor condition.

Searchers found kayaks that had been towed by the boat as well as a debris field about 37 miles offshore. It included six life vests, a basketball, propane tank, tennis shoes and several water bottles, which Kimberly's brother identified as belonging to his relatives.

The search has also involved several state and local maritime emergency responders. It will continue through the night.

(Reporting by Laila Kearney in New York and Ian Simpson in Washington; Editing by Bernadette Baum and Matthew Lewis)