Mutko, who served as Russia's sports minister from 2008 to 2016, made the same comment ahead of the 2016 Rio Olympics, when Russia's participation was in limbo over allegations of state-sponsored doping.
The Pyeongchang organising committee said Wednesday it would prefer if Russians competed under their own flag, but accepted as "second-best" the decision to allow their participation as neutrals.
Russian athletes competing will carry a neutral flag and the name "Olympic Athlete from Russia." the IOC says.
"To participate in the Olympics is an athlete's right".
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The IOC on Tuesday banned Russian Federation from the Olympics after evidence emerged of an "unprecedented systematic manipulation" of the anti-doping system. "I think time will settle everything down".
Russia's athletics federation and Paralympic Committee remain suspended from global competition over doping scandals, along with its anti-doping agency, RUSADA.
"We will all know that they will be representing Russian Federation".
The statement came after Russian President Vladimir Putin said Moscow would not boycott the event despite the ban over a state-orchestrated doping programme, assuaging fears Russia could spurn the Games entirely.
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The Russian team has been stripped of 11 of the 33 medals it won at the $50 billion Sochi Games, the most expensive in history, because of doping violations, knocking it from first to fifth place in the overall medals ranking.
"I also feel concerned for the guys, many of whom I know personally and consider them to be my friends", Putin said adding that all of them will have to make an important decision now. "But here, their country kind of went beyond what they needed to do to help their athletes improve their game".
"Requirements for Russian athletes are being particularly emphasized by the pre-Games testing task force, because of the situation and work of the commissions", he said.
"With the Olympic Truce resolution, the UN General Assembly is creating the conditions for all athletes to compete in peace".
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Prof Muigai said the government would not stop at anything to prevent the breach of the rule of law and the constitution. Kenya's Attorney General Githu Muigai speaks during a press conference in Nairobi, Kenya September 22, 2017.