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Authorities say the group of six was flying from La Romana in the Dominican Republic to San Juan, Puerto Rico. All are U.S. citizens.
Witnesses reported seeing an explosion on the Cessna 206 before it fell into the Atlantic Ocean off the island's northern coast.
Coast Guard spokesman Ricardo Castrodad said that authorities have located what appears to be the wreckage in waters off the northwestern city of Quebradillas. Helicopters and boats have been searching for survivors.
CNN notes that five searches were conducted on Sunday and two during the evening. Three more searches are scheduled for Monday.
The private plane was chartered by Tropical Aviation Corp. The names of the pilot and passengers have not been released pending notification of family, but the passengers were San Juan residents, according to reports.