The Associated Press reports four people were on board.
The Coast Guard and local police are searching for the remaining crash victims.
Only two bodies had been recovered as of early Sunday, but all four of the plane's occupants are presumed dead.
East Hampton Town Police identified the people on board as 70-year-old builder Bernard Krupinski, 70-year-old Bonnie Krupinski, 22-year-old William Maerov and 47-year-old Jon Dollard. With four people aboard, the plane lost communication with the East Hampton Airport control tower and then failed to land at the airport.
The cause of the plane crash remains unclear.
The plane went down about a mile off the Long Island coastline near Indian Wells Beach on Saturday afternoon around 2:50 p.m., according to the New York Post. "I can't confirm that was the cause", he said on Saturday afternoon.More news: Vehicle drives onto ME field during baseball game, 1 man killed
It marks the second small plane crash on Long Island this week.
A rescue and recovery effort is underway with police, the Coast Guard, and the Air National Guard participating, the police chief said.
Mr. O'Hare added that multiple fishing vessels were also on the scene. The plane went down about a mile and a half off the coast of Indian Wells Beach in Amagansett.
Anyone with information has been encouraged to contact the Coast Guard Sector Long Island Sound command center at 203-468-4401 or on the radio at VHF-FM marine radio channel 16.
In a separate statement, Amos Goodman, chairman for the East Hampton Town Republican Committee, said, "Bonnie and Ben Krupinski were two great pillars of our community, who embodied the values of our town: generosity, warmth, charity, kindness, and hard work".