The search covered more than 33 hours and saturated a 646 square-mile area before it was called off, the Coast Guard said.
The Associated Press reports four people were on board.
East Hampton town police say the four people on board included Ben and Bonnie Krupinski, both 70 years old, and their grandson, 22-year-old William Maerov, of East Hampton.
Krupinski, a East Hampton native, was a well-known businessman who built luxury homes for Martha Stewart and for Billy Joel and Christie Brinkley, among others, according to his website. The Federal Aviation Administration said the aircraft went down around 3:20 p.m. Saturday, approximately two miles off the shore near Indian Wells Beach in Amagansett.
The cause of the crash is unknown..
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The cause of the crash is under investigation.
Grieving loved ones hunkered down at the Krupinski compound in East Hampton, with private security guards turning away reporters.
East Hampton Town Police Chief Michael Sarlo said that while the Coast Guard continues the search with its larger vessels throughout the night, a "full-scale operation will resume at daybreak". The plane apparently lost contact with the East Hampton Airport about a mile south of the airport before it crashed, the East Hampton Star reported. Two bodies have been pulled from the water so far.
Sector Long Island Sound issued an Urgent Marine Information Broadcast notice to mariners, requesting boats in the area to keep a sharp lookout for the crashed plane and any survivors. The plane was en route to East Hampton Airport, when it appears to have flown directly into a thunderstorm.