The 69-year-old Italian’s position had been in doubt since Russia lost a European Qualifier to Austria this month, leaving them third in Group G and struggling to reach the finals.
His current contract is due to end after the 2018 World Cup finals, which are due to take place in Russia.
Russia’s former FIFA vice-president Vyacheslav Koloskov had claimed that Capello would be removed as boss at Wednesday’s meeting.
But, RFS acting president Nikita Simonyan told Russian News Agency Tass that the Italian remained in his post after the meeting, which was held behind closed doors, and would meet RFS bosses “on the subject of either continuing to work or a separation”.
Arsenal shareholder Alisher Usmanov has given the RFS around £3.5m to pay salary arrears owed to Capello.
As a member of the Russia 2018 Local Organising Committee Supervisory Board, Usmanov decided to give financial help to the RFS to the tune of 300 million roubles,” Usmanov’s press service confirmed.
“Ahead of the 2018 World Cup, the question regarding the head coach is of great importance for the national football team.”
Russia lost their most recent European Qualifier 1-0 at home to Austria, with Capello’s side having won just two of their last 10 competitive fixtures.
One of those came against Liechtenstein and the supporters were so disgruntled by the results that they started to try and part-raise the £15.5m required to buy Capello out of his contract, before Usmanov stepped in.