Jeanne Bernard Pierre, the director-general of Haiti's National Migration Office, said the migrants' account hasn't been confirmed but that the Haitian government would consider it "criminal" if found true.
The death toll rose to 61 Tuesday from Friday's pre-dawn capsizing of the migrant-laden sailboat off the British Caribbean territory of Turks and Caicos, after more bodies were found drifting in the Atlantic Ocean, the Turks and Caicos government said Tuesday.
The migrants' bodies were spotted by a police boat and fishermen in shark-filled waters near where their overloaded sloop overturned, Turks and Caicos Gov. Richard Tauwhare told a news conference.
"We are making every effort we can to identify the bodies," Tauwhare said, adding that two U.S. pathologists were conducting autopsies on the badly decomposed remains.
More than a dozen other Haitian migrants were missing and presumed dead. Officials estimate about 160 people were on board.
Tauwhare said that the vessel overturned while it was being towed to shore by a Turks and Caicos police boat during a storm. The government had previously said authorities arrived on the scene only after it sank.
Seventy-eight survivors — 69 men and nine women — were being housed in a detention center until they can be flown back to Haiti.
Every year, hundreds of Haitians set off in rickety boats, fleeing economic and civil disorder in the Western Hemisphere's poorest nation in hopes of finding a better life by sneaking into the United States or other Caribbean islands.