The pilots of the An-148 regional jet did not report any problems before the twin-engine aircraft plunged into the field about 40 kilometers (25 miles) from Domodedovo Airport, authorities said.
The Saratov Airlines flight disappeared from radar just minutes after departure for the city of Orsk, some 1,500 kilometers (1,000 miles) to the southeast.
Transport Minister Maxim Sokolov confirmed that there were no survivors.
The 65 passengers ranged in age from 5 to 79, according to a list posted by the Russian Emergencies Ministry, which did not give their nationalities. Six crew members were also aboard.
Emergency workers combed through the field while investigators descended on the airport to search for clues to what brought the jet down. One of the flight recorders was recovered, Russian news reports said, but it was not immediately clear if it was the data or voice recorder.
The airport has been the focus of security concerns in the past. Security lapses came under sharp criticism in 2004, after Chechen suicide bombers destroyed two airliners that took off from the airport on the same evening, killing a total of 90 people. A 2011 bombing in the arrivals area killed 37 people.
Investigators also conducted a search at the airline's main office in Saratov, reports said.
In Washington, The Trump administration has expressed sympathy for the families of the 71 people killed in the crash. White House press secretary Sarah Huckabee Sanders said the U.S. "is deeply saddened by the tragic deaths of those on board Saratov Airlines Flight 703."
Russia's Investigative Committee said all possible causes were being considered. Some reports suggested there were questions about whether the plane had been properly de-iced. Moderate snow was falling in much of Moscow at the time of the crash.
Airline spokeswoman Elena Voronova told the state news agency RIA Novosti that one of the pilots had more than 5,000 hours of flying time, 2,800 of them in an An-148. The other pilot had 812 hours of experience, largely in that model plane.
Tass said the plane entered service in 2010 for a different airline, but was held out of service for two years because of a parts shortage. It resumed flying in 2015 and joined Saratov's fleet a year ago.
TV footage from the crash site showed airplane fragments lying in the snow. Reports said the pieces were strewn over an area about a kilometer (0.6 miles) wide.
A plane can disappear from radar when it gets too close to the ground to reflect radar signals.
John Cox, a former airline pilot and now a US-based safety consultant, said the disappearance could also indicate that the jet's transponder lost power.
"That says potential of engine failure or a technical problem," Cox told The Associated Press.
President Vladimir Putin put off a planned trip to Sochi to monitor the investigation. Putin was to meet Monday with Palestinian leader Mahmoud Abbas at the Black Sea resort, where the president has an official residence.
Instead, Abbas will meet with Putin in Moscow in the latter part of Monday, Kremlin spokesman Dmitry Peskov told Russian news agencies.
The An-148 was developed by Ukraine's Antonov company in the early 2000s and manufactured in both Ukraine and Russia.
Shabby equipment and poor supervision plagued Russian civil aviation for years after the 1991 collapse of the Soviet Union, but its safety record has improved in recent years.
The last large-scale crash in Russia occurred on Dec. 25, 2016, when a Tu-154 operated by the Russian Defense Ministry on its way to Syria crashed into the Black Sea minutes after takeoff from Sochi. All 92 people on board were killed.
In March 2016, a Boeing 737-800 flown by FlyDubai crashed while landing at Rostov-on-Don, killing all 62 people aboard.
An onboard bomb destroyed a Russian Metrojet airliner in October 2015 soon after it took off from Egypt's Sharm al-Sheikh resort. The bombing killed 224 people.
Jocelyn Gecker in San Francisco contributed to this story.
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