"There were 78 people including crew members on board the plane," the Investigative Committee said in a statement, adding it had headed to the northwest Russian city of Murmansk.
"According to the updated info which the investigation has as of now, 37 people survived." Another 11 people were injured, Dmitry Matveyev, the Moscow region's health minister said earlier in the day.
Three of them had been hospitalised but they were not in a serious condition, he added.
Investigators said they were looking into various lines of inquiry and it was premature to draw any conclusions about the cause of the accident.
Russian President Vladimir Putin had offered his condolences to the victims' loved ones, his spokesman Dmitry Peskov said.
Prime Minister Dmitry Medvedev has also ordered a special committee to investigate the disaster.
The jet carrying 73 passengers and five crew members had just left Sheremetyevo when the crew issued a distress signal, officials said.
"Flight Su-1492 took off on schedule at 6:02 pm (15H02 GMT)," said a statement from the airport.
"After the take-off, the crew reported an anomaly and decided to come back to the departure airport. At 6:30 pm, the aircraft made an emergency landing," it added.
The tabloid newspaper Komsomolskaya Pravda quoted one passenger, Petr Egorov, who said: "We had just taken off and the aircraft was hit by lightning.... The landing was rough, I almost passed out from fear." "The plane sent out a distress signal after takeoff," a source told Interfax news agency.
"It attempted an emergency landing but did not succeed the first time, and on the second time the landing gear hit (the ground), then the nose did, and it caught fire," the source added.
Interfax, citing an anonymous source, said the plane had landed with its fuel tanks full because, having lost contact with air traffic controllers, it was too dangerous to dump its fuel tanks over Moscow.
Several flights have been diverted to other Moscow airports or Nizhny Novgorod, some 500 kilometres (310 miles) east of the Russian capital.
The Sukhoi Superjet-100 was the first civilian aircraft developed in Russia's post-Soviet era and at the time of its launch, in 2011, was a source of national pride.
But it struggled to convince buyers from airlines outside Russia, and several foreign carriers that did buy it have since prefered to cut back its use or phase it out completely, citing its reliability.
The Russian government offered subsidies to encourage Russian airlines to buy the Superjet and Aeroflot became its main operator. In September 2018, it announced a record order of 100 Superjet-100s.
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