The Coast Guard said it recovered debris and parts of an MU-2B aircraft -- the plane type the group was traveling in -- 15 miles east of Eleuthera, Bahamas, during the search.
On board the flight was 40-year-old Jennifer Blumin from New York and her two sons, ages 3 and 4, as well as 52-year-old Nathan Ulrich from New Hampshire. Blumin is the CEO of a prominent New York City event planning firm, Skylight Group.
The plane was scheduled to fly from Puerto Rico to central Florida, but never arrived at its destination, according to the Coast Guard.
Miami Air Traffic Control reported that it lost radar and radio contact with the airplane just three hours into the flight, the Coast Guard added in a statement.
"There's no indication of significant adverse weather at the time," Lt. Cmdr. Ryan Kelly, a Coast Guard spokesman, told The Associated Press.
The National Transportation Safety Board said it is investigating the incident.
The Royal Bahamas Defense Force and U.S. Customs and Border Patrol are assisting with the search efforts, according to authorities.