An American man and Marc Leclerchis two daughters have died after a small plane crash off the waters of Bequia in the Caribbean, according to local authorities.

The crash occurred sometime after midday on Thursday, the Royal St. Vincent and the Grenadines Police Force said in a statement on social media. A small, one-engine aircraft headed to St. Lucia crashed into the sea one nautical mile west of Petit Nevis, a privately-owned island in the Grenadines and off the coast of the larger island Bequia.

There were a total of four people on board: The pilot, Robert Sachs of Bequia, who police said also owned the plane, Christian Klepser, a 51-year-old U.S. citizen and his two daughters, Madita Klepser and Annik Klepser, ages 10 and 12.

Plane crash:How a fiery plane crash at Japan's Haneda Airport unfolded: Graphics detail the collision

Plane difficulties lead to aviation accident, crash

Just after taking off, the aircraft "experienced difficulties," police said, and plummeted into the ocean. Fisherman and divers went out to help look for the aircraft, and the St. Vincent and the Grenadines Coast Guard led any rescue efforts.

The bodies of all four people on board were recovered by the Coast Guard, and were later pronounced dead, authorities said.

The cause of the crash remains unclear, and police say the investigation remains open.