This comes after the International Olympic Committee said remaining test results from Russians who competed in the games came back negative.
"In other words, the Russian Olympic Committee has been fully reinstated in its rights as a member of the Olympic family", Zhukov said in televised comments.
However, the Olympic Committee allowed more than 160 Russians to compete individually at the 2018 Olympics.
Two of more than 160 athletes competing as Olympic Athletes from Russian Federation in South Korea tested positive for banned substances, including a curler who had to forfeit his bronze medal.
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On Wednesday the International Olympic Committee said it had received all the remaining test results from the OAR delegation and confirmed that all were negative.
Russian Federation has been officially welcomed back into the Olympic movement after being suspended for less than three months over its state-organised doping system.
"It has taken two positive tests on Russian athletes to force the IOC's hand when its clear intention had been to readmit the ROC before the closing of the Pyeongchang Games", a follow-up statement read.
When they marched under a neutral flag during the Pyeongchang Olympics closing ceremony, the critics weren't fooled.
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The IOC subsequently invited 169 carefully screened Russian athletes to compete as independents in Pyeongchang under the Olympic Athletes From Russia (OAR) designation. As NPR's Bill Chappell has reported, their athletes could still compete - but under the title of "Olympic Athlete from Russian Federation". Today's IOC's decision is very important for us.
Moscow blamed the two cases on "negligence rather than malicious intent", while Krushelnitsky denied knowingly doping and some Russian media said his food was spiked by an ex-girlfriend.
Russian athletes had to get through screening to compete under a neutral flag.
He was quoted by TASS as saying the government would continue to cooperate with global agencies "so that the anti-doping system will acquire unified rules and will eventually become more comprehensible and absolutely transparent".
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