Annie Hayat said the plane flown by 17-year-old Haris Suleman went down shortly after leaving Pago Pago in American Samoa on Tuesday night. Suleman and his father, Babar Suleman, were on board.
Hayat said the body of Haris Suleman had been recovered, but crews were still looking for his father.
US Federal Aviation Administration spokesperson Ian Gregor in Los Angeles said the single-engine Hawker Beechcraft plane crashed into the ocean on Tuesday night under unknown circumstances.
The tail number provided by the FAA shows the plane is registered to a limited liability corporation whose address matches Babar Suleman's home address in Plainfield, Indiana.
US Coast Guard spokesperson Petty Officer Melissa McKenzie said witnesses reported seeing the Honolulu-bound plane crash about a mile from shore shortly after taking off from Pago Pago International Airport.
The Sulemans left the state on 19 June in hopes of making the trip in 30 days to set the record for the fastest circumnavigation around the world in a single-engine airplane with the youngest pilot in command to do so.
The trip was also raising money for the Citizens Foundation, a nonprofit that builds schools in Pakistan.
They planned to return home on Sunday.