The International Olympic Committee on Monday sanctioned five Russian athletes, including two four-man bobsleigh champions and two biathlon silver medallists, following recommendations from the Oswald Commission into the doping scandal.
"The Russian Bobsleigh Federation and the Cross Country Ski Federation of Russia are ready to appeal at the Court for Arbitration for Sport (CAS)," the ministry said in a statement quoted by the Interfax press agency.
Athletes "have no intention of turning in their medals" before the appeal, the statement added.
Kremlin spokesman Dmitry Peskov decried the "baseless decisions" of the IOC and promised to "defend our athletes actively and with energy".
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Russia has been stripped of 11 of its 33 medals from the event, meaning the country has lost its position at the top of the table to Norway.
The IOC is due to decide next week whether Russia will be allowed to participate at the Pyeongchang Games in February.
An explosive 2016 report commissioned by the World Anti- Doping Agency alleged state-sponsored doping in Russia and saw the country shut out of the agency.
Russia has consistently denied running a doping programme.