TASS wrote at least 13 people have died in the accident and another six were injured.
Dramatic footage shared on social media showed the Russian Aeroflot-owned aircraft, flames and black smoke pouring from its fuselage, land at Sheremetyevo worldwide airport.
It's unclear what caused the fire.
Video footage showed desperate passengers leaping out of the plane onto an inflatable evacuation slide and staggering across the airport's tarmac and grass, some holding luggage.
"The plane turned back and there was a hard landing".
Earlier, the Russian Investigative Committee confirmed that 13 people, including two children, had died.
The tabloid newspaper Komsomolskaya Pravda quoted one passenger, Petr Egorov, who said: "We had just taken off and the aircraft was hit by lightning".
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Terrified passengers were seen fleeing the Russian national carrier Aeroflot plane as flames flared from the rear of the aircraft with a reported 78 on board.
This image taken from video and provided on the Twitter feed of Mikhail Norenko shows smoke from a plane on fire at Moscow's Sheremetyevo International Airport on Sunday.
A rescue team was combing through the charred wreckage of the rear of the plane on Sunday evening looking for survivors, the Interfax news agency reported.
As it stands, one runway is now still in use at the airport, but some flights are diverting to other airports as a result of the crash landing.
Reports of multiple injuries and fatalities are emerging from media sources, but an official death toll has yet to be released.
According to the play-back of the flightradar data, made by Bloger51 in Murmansk, the plane was in the air for 27 minutes. The entire tail was then in blaze and black smoke billowed from the plane.
Russian news agencies said the pilots landed on their second attempt.