The search was called off at 8:45 p.m. Thursday for the four, 15 miles east of Eleuthera.
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Missing are Jennifer Blumin, 40, from New York City, pilot Nathan Ulrich, 52, from Lee, New Hampshire, and Blumin's 3-year-old and 4-year-old sons.
"This was a swift and significant loss and its impact has reverberated through everyone that participated in the search," said Christopher Eddy, search and rescue mission coordinator.
The plane was traveling from Puerto Rico to Florida Tuesday when air traffic control in Miami lost contact with the twin-engine MU-2B aircraft.
Their plane was at about 24,000 feet when air traffic control lost contact. The area is commonly known as the Bermuda Triangle.
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A Coast Guard official said authorities found debris from the same kind of plane that disappeared.
A mechanic, who previously worked on the plane carrying the group, was examining the parts to determine whether they're from the specific plane.
Blumin is founder and CEO of Skylight Group, which provides event space around New York City, specializing in the fashion industry.