Two bodies have been pulled from the water so far. Their identities have not yet been released.
Meanwhile authorities have released the names of all four passengers who were on board the plane, including a prominent builder for celebrities' homes.
The FAA reports the aircraft crashed two miles off the shore of Indian Wells Beach in Amagansett just before 3 p.m. Saturday.
The plane was a Piper PA31 Navajo twin-engine aircraft with four people on board including the pilot, reports the Coast Guard.
Roadblock at Indian Wells Beach as search continues offshore for two victims of #Amagansett, LI plane crash. Two male bodies recovered amid debris field. Police not confirming identities of those onboard Piper twin-engine turboprop. @ABC7NY pic.twitter.com/r42Dc7xy6w— N. J. Burkett (@njburkett7) June 3, 2018
East Hampton Town police have identified 70-year-old Bernard Krupinski and 70-year-old Bonnie Krupinski as two of those who were on the plane.
Their grandson, 22-year-old William Macrov, was also on board along with the pilot, identified as 47-year-old Jon Dollard.
The plane was en route to East Hampton Airport, when it appears to have flown directly into a thunderstorm. When the plane fell off the radar screens, controllers called police.
The NTSB is looking into the cause of the crash.
The Coast Guard and local police were assisted by crews from commercial fishing boats in searching for the victims. The search covered more than 33 hours and saturated a 646 square-mile area before it was called off, the Coast Guard said.
Bernard Krupinski grew up in East Hampton before starting his business, Ben Krupinski Builders, there. As a builder, his clients included Martha Stewart and Billy Joel.
(The Associated Press contributed to this report.)
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