It cited Anna Antseliovich, the acting director general of RUSADA, as making the admission in an interview.
"It was an institutional conspiracy," it cited her as saying. She said top officials had not been involved.
That appeared to chime with the final part of the World Anti-Doping Agency's independent report into doping which this month provided evidence of an elaborate doping scheme.
The report found more than 1,000 Russian competitors in more than 30 sports were involved in a conspiracy to conceal positive drug tests over a period of five years.
But RUSADA said in a statement on Wednesday that Antseliovich's words, as reported in the New York Times, had been "distorted" and "taken out of context."
"We want to underline that RUSADA does not have and could not have the authority to admit or deny such a fact (of an institutional conspiracy)," RUSADA said.
"The Russian Federation's Investigative Committee is looking into the matter (of doping). Every accused sports person has the indisputable right to object to the accusations."
Kremlin spokesman Dmitry Peskov told reporters Russian authorities had always denied that the Russian state had been involved in doping.
Russian President Vladimir Putin said last week there were some problems with sports doping in Russia, but that there was no state-sponsored doping system as critics have alleged.
Sports should not be politicised, said Putin.
More than 100 Russian athletes were barred from competing at the Olympics in Rio de Janeiro this year after the International Olympic Committee set criteria for Russian athletes to meet, including a clean doping past and sufficient testing at international events.
(Reporting by Amlan Chakraborty in New Delhi, Denis Pinchuk, Peter Hobson and Andrew Osborn in Moscow; Editing by Jason Neely and Janet Lawrence)
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