The Russian Football Federation submitted an appeal to the sports arbitration court, Cas, on Thursday.
They believe that Fifa and Uefa have no legal right to suspend them from international matches and tournaments.
Now they demand that the matter be taken up - and it should go quickly.
"To ensure the possibility for Russian teams to participate in the upcoming scheduled matches, the Russian Football Association will insist on an accelerated handling of the matter.
If Fifa and Uefa refuse such a procedure, a demand will be made for the introduction of temporary measures in the form of a repeal of Fifa's and Uefa's joint decision ", the Russian Federation writes in a press release.
Furthermore, the Russian Federation writes that they were not given the right to express their position before a decision was taken on the matter and that that procedure violated their fundamental right to a defense.