* Fifteen bodies found after wreck off Turks and Caicos
* Haitian migrants' boat hit reef late on Sunday and sank
* Repatriation of over 120 surviving migrants has begun (Updates with more bodies found, repatriation started)
MIAMI, July 28 (Reuters) - At least 15 Haitian migrants drowned and more than 65 were missing after their wooden sail boat hit a reef and sank off the Turks and Caicos islands, local police and the U.S. Coast Guard said on Tuesday.
More than 120 people were rescued following the shipwreck late on Sunday, and Coast Guard cutters and aircraft were assisting Turks and Caicos authorities in the search for more survivors.
Police in the British territory said 15 bodies had been recovered in waters off West Caicos, a sparsely inhabited island popular with divers and boaters.
"Our search is continuing, by sea and air," Petty Officer Nick Ameen said in Miami. "As time progresses, the possibility for survival diminishes," he added.
Turks and Caicos police spokesman Sergeant Calvin Chase said there were conflicting reports about how many people had been on board the wooden sloop, which he said was carrying illegal migrants from Haiti trying to reach the United States.
Estimates given earlier by the Coast Guard ranged from 160 to 200.
"The boat ran aground on a reef, Molasses Reef, off West Caicos," Chase told Reuters by phone. "We have a total of 15 dead bodies now," he added. Earlier, he said 122 migrants -- 22 women and the rest men -- had been rescued.
"They are illegal immigrants," Chase said, adding the repatriation of the survivors back to Haiti had already begun.
Coast Guard vessels and helicopters, the Turks and Caicos Police Marine Patrol and private boats had all helped pluck the survivors from the reefs and waters on Monday.
Haitian migrants often leave their impoverished Caribbean country in dangerously crowded boats, hoping to escape poverty and find work in the Bahamas or Florida.
The Turks and Caicos islands are a British territory in the Atlantic Ocean, between the southern Bahamas and the north coast of Haiti.
The Coast Guard said some of the most gravely injured survivors were taken by helicopter to the Turks and Caicos capital of Providenciales for medical treatment.
Last week, the Coast Guard intercepted 124 Haitian migrants from what they called a "grossly overloaded" 60-foot (18-metre) boat about 150 miles (240 km) southwest of the shipwreck site. They were repatriated to Haiti on Monday.
Reporting by Pascal Fletcher and Jane Sutton in Miami, Deborah Charles in Washington; Editing by Vicki Allen
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