Fragments of the plane were found near the village of Stepanovskoye in the Moscow Region's Ramensky district.
The plane is believed to have been fully intact until the moment of impact, when it exploded and strewed wreckage across the snowy field in which it crashed.
Investigators said the plane's crew did not report any technical problems before the crash.
Investigators said they had opened a criminal case into the incident and were looking at all possibilities.
Rouhani also wished health and success for President Putin and glory for the Russian people and government. The Kremlin said U.S. President Donald Trump called Putin to express his condolences.
Transport Minister Maxim Sokolov said Monday the search for victims' remains will take a week.
Most of the victims were from Orsk, where the authorities declared official mourning Monday. According to the TASS news agency, it was put out service for two years due to parts shortage, before resuming operations in 2015. Saratov Airlines commissioned it a year ago.
The plane's captain reportedly didn't want to defrost the aircraft before flying.
"[The] explosion occurred after the aircraft had come down", it adds.
It was developed by Ukraine's Antonov company in the early 2000s. At least eight passengers were from other parts of Russian Federation, and four of the crew were from Saratov.
Some regional carriers in Russian Federation reportedly have cut corners on servicing aircraft. According to preliminary data, there were 65 passengers and six crew members aboard the plane.
Pilot error was blamed for that crash.
Along with several commercial carriers, the An-148 is operated by the Russian Defense Ministry and several other government agencies.
Both of the black boxes have been recovered from the crash site for analysis.