The New York City Police Department (NYPD) recovered a body, presumed to be the pilot, from the river and near the plane that crashed on Friday evening, an NYPD spokesman said.
A distress signal was sent before the crash, CNN reported citing the spokesman as saying.
The P-47 Thunderbolt was one of three aircraft that departed Republic Airport on Long Island, according to Kathleen Bergen, spokeswoman for the Federal Aviation Administration.
It was unclear whether the plane was in the area for an air show at Jones Beach State Park on Long Island.
According to the Smithsonian National Air and Space Museum, the Thunderbolt was a feared ground-attack aircraft.
“US Army Air Forces commanders considered it one of the three premier American fighters, along with the P-51 Mustang and P-38 Lightning. The US built more P-47s than any other fighter airplane,” the Smithsonian said.