The Associated Press reports four people were on board.
Update, 9:30 p.m.: The search for two missing people from a plane crash off the Amagansett shoreline Saturday afternoon will continue into the night, weather permitting, a United States Coast Guard spokesman said Saturday evening.
As of Sunday afternoon, authorities had recovered two bodies, but their identities had not been released, the newspaper reports.
East Hampton Police say Bernard Krupinski, 70, his wife Bonnie Krupinski, 70, their grandson William Maerov, 22, and pilot John Dollard, 47, were on the plane when it crashed.
Captain Anderson said the Federal Aviation Administration is investigating the cause of the crash.
Mr. O'Hare could not identify a cause of the plane crash, only offering that it was around the time that thunderstorms had entered the area.More news: Brazil vs. Croatia - Football Match Report
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"I will miss each of them so very, very much", Stewart said.
Two bodies were recovered from the scene, WABC-TV reported.
The aircraft was about one mile away from the airport when it lost contact with the East Hampton Tower, the East Hampton Police Department said. The plane went down about a mile and a half off the coast of Indian Wells Beach in Amagansett.
East Hampton, where the plane crashed, and the nearby towns on eastern Long Island are known for the many wealthy and prominent individuals who spend their summers there, including stars such as Alec Baldwin and Gwyneth Paltrow.
Saturday's deadly crash marked the second small plane crash on Long Island in a week.
This article will be updated with more information as it is available.