According to Russian news agencies, 65 passengers and 6 crew members were on board and all were feared dead.
The governor of the Orenburg region, where the plane was flying to, told Russian media that "more than 60 people" onboard the plane were from the region.
Alexander Neradko, the head of Rosaviatsiya, the state agency overseeing civil aviation, said it will make a detailed scrutiny of Saratov Airlines' operations, but he added that the company had a decent record.
Saratov Airlines flight 6W703 came down just minutes after taking off from Moscow's Domodedovo airport, crashing roughly 80km south of Moscow near the town of Argunovo.
A regional official said the black box had been retrieved from the wreckage.
The transport ministry said several causes for the crash are being considered, including weather conditions and human error.
"Eyewitnesses have said they saw the plane crash into the ground and was reportedly on fire", The Daily Star reported.
The mystic thought the spirits were urging him to cancel his birthday party but in fact they were warning him against boarding the doomed Russian jet, the Mirror reported.
"The Saratov Airlines plane (flight 730 from Moscow to Orsk) took off at 14.21 Moscow time".
Tass said the plane entered service in 2010 for a different airline, but was taken out of service for two years because of a parts shortage. On appeal, the carrier resumed worldwide flight operations in May 2016.
Russian President Vladimir Putin delayed his plans to visit the Olympic Games in PyeongChang to monitor the investigation.
Emergency vehicles at the site of the crash in the evening after it happened.
All 71 people on board the flight were killed when it crashed into a field.