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 US Army helicopter.
US 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 US 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.
"They were my favourite sports people. They were part of my first attempt at the world championships and became champions in 1994. They were talented and beautiful people," said Velikova, visibly distraught.
"Apart from anything else they were my children. Zhenya (Shishkova) trained with me from the age of 11 and Vladik (Naumov) from age 14. They were like my own children. What's happened is awful. The best people have been taken away from us."
Inna Volyanskaya, a former skater who competed for the pre-1991 Soviet Union, was also reported to have been on board the plane, TASS said. She was a coach at the Washington Figure Skating Club, according to its website.
The Kremlin expressed its condolences to the families of Russian citizens who lost their lives in the crash and said the news that Shishkova and Naumov had been on board appeared to be confirmed.
"There were other of our fellow citizens on board. It's bad news today from Washington. We are sorry and send our condolences to families and friends," Kremlin spokesman Dmitry Peskov told reporters.
Russia's figure skating federation voiced its condolences to those who had lost loved ones in the crash but said it was unable to comment further.
"We are devastated by this unspeakable tragedy and hold the victims' families closely in our hearts," US Figure Skating said in a statement.
SKATERS HAD JUST COMPETED IN WORLD CHAMPIONSHIPS
More than 180 athletes competed in the Jan. 20-26 championships in Kansas, the organisation said. The development camp was held Jan. 27-28 for nearly 150 up-and-coming skaters across performance levels, the US Figure Skating website said.
The International Skating Union (ISU) said it was "deeply shocked by the tragic accident".
"We are heartbroken to learn that figure skaters, along with their families, friends, and coaches, are understood to be among those on board," the global governing body said in a statement. "Our thoughts are with everyone affected by this tragedy.
"Figure skating is more than a sport - it's a close-knit family - and we stand together. We remain in close contact with US Figure Skating and offer our full support during this incredibly difficult time."
Officials have not said how many people died in Wednesday night's midair crash between the airliner and helicopter but suggested that there might be no survivors.
In 1961, the 18-member US figure skating team died in a plane crash en route to the world championships in Prague.