The plane, with 64 passengers and crew, was en route to Washington, D.C., from Witchita, Kansas, when it was involved in a mid-air collision with a U.S. Army helicopter.
U.S. Figure Skating, the governing body for figure skating in the United States, said athletes, coaches and family members were returning from the National Development Camp held in conjunction with the U.S. Figure Skating Championships in Kansas.
"We are devastated by this unspeakable tragedy and hold the victims’ families closely in our hearts," it said in a statement.
A source told Reuters that as many as 15 people on the flight may have been involved in figure skating.
Officials have not said how many people died in the accident but have suggested that there may be no survivors.
Russian state media meanwhile reported that ice skating coaches and former world champions Evgenia Shishkova and Vadim Naumov were among those on board the plane. Their son, Maxim, also a skater, may also have been on the plane, Russia's TASS and RIA news agencies reported.
Inna Volyanskaya, a former skater who competed for the Soviet Union, was also reported to have been on board, TASS said. She was a coach at the Washington figure skating club, according to its website.