Svetlana Kryshtanovskaya, an aide to Igor Levitin, Russia's transport minister, said: "On take off there was a flare up in the area of the engine. The aircraft fell onto the runway and broke up."
Khikmatov said the aircraft belonged to a US company he identified as Ford-Aero.
The US embassy said it could not immediately confirm that the crew were Americans.
Moscow was enveloped in snow on Tuesday and Fyodorov said visibility was about 1,200 metres at the time of the crash.
Vnukovo was shut after the accident and the jet was being removed from the runway, Russian news agencies reported.