The International Olympic Committee (IOC) this month annulled the results of 14 Russian athletes who competed in Sochi because of doping violations.
They were stripped of their medals and banned for life from participating in future Olympics.
The decisions followed an IOC investigation into allegations of state-backed doping among Russian competitors and sample tampering by laboratory and security officials at Sochi.
"The main thing is to persistently and energetically take all possible measures to protect our legitimate interests and the legitimate interests of our athletes together with international sports organisations," Kremlin spokesman Dmitry Peskov told reporters at a conference call.
"One can hardly steal a victory that has already been won, especially a victory that will forever stay with our hero athletes," he said.
Russia was first in the medal table at the end of the Games but the IOC decisions bring down their number of gold medals to nine, behind Canada and Norway.
The bans have so far targeted athletes in four disciplines: cross-country skiing, skeleton, bobsleigh and speed skating.
Those banned and stripped of their medals include double gold medallist Alexander Zubkov, who also serves as president of Russia's bobsleigh federation, and cross country skier Alexander Legkov, who won gold in the 50km freestyle and a silver medal in the 4x10km relay event.
Peskov did not spell out what measures Russia could take. But the federations governing these sports in Russia have said they will seek to contest the IOC's decisions at the Court of Arbitration for Sport (CAS).
Despite calls to cooperate with international bodies to help rid Russia of doping, the Russian authorities have never acknowledged any state role in the scandal.
The IOC is re-testing all Russian athletes' samples from the 2014 Games following revelations by Grigory Rodchenkov, the former head of Moscow's discredited anti-doping laboratory, of a scheme to cover up home competitors' positive samples.
The Sochi scandal is part of a broader doping affair that has led to the suspension of Russia's anti-doping agency RUSADA, its athletics federation and Paralympic Committee.
The IOC has said it would decide during its executive board meeting next month on the participation of Russian competitors at the Pyeongchang Winter Olympics in February.
(Reporting by Maria Tsvetkova; Editing by Maria Kiselyova, Gabrielle Tetrault-Farber and Richard Balmforth)
