American actor Christian Oliver and his two daughters have died in a plane crash near a small private island in the eastern Caribbean, police in St. Vincent and the Grenadines said.

The crash occurred Thursday just west of Petit Nevis Island, near Bequia, as the plane was en route to nearby St. Lucia, police said in a statement.

They identified the daughters as 10-year-old Madita Klepser and 12-year-old Annik Klepser, adding that the pilot, Robert Sachs, was also killed.

The cause of the crash had not yet been established, authorities said.

Fishermen and divers from the area rushed to the crash site to help as the St. Vincent and the Grenadines Coast Guard made its way to the area.

Christian Oliver and his family at a premiere in 2015.CHRIS DELMASAFP

"The selfless and courageous acts of fishermen and divers are greatly appreciated," police said.

The 51-year-old German-born actor had dozens of film and television roles, including the 2008 film "Speed Racer" and Steven Soderbergh's 2006 World War II film "The Good German," starring George Clooney and Cate Blanchett.

Oliver starred in the second season of the 1990s series "Saved by the Bell: The New Class," playing a Swiss exchange student named Brian Keller.