"It was an institutional conspiracy," the newspaper quoted Anna Antseliovich as saying.
New York Times spokeswoman Danielle Rhoades Ha responded to Antseliovich's accusation that a reporter misrepresented her words.
"We are confident in the accuracy of our story, which quotes Ms. Antseliovich fairly, accurately and extensively," she told CNN.
The Times story sparked push-back from Kremlin spokesman Dimitry Peskov. "We categorically deny it," he said.
Reporter Rebecca R. Ruiz wrote in the article that over several days of interviews with the Times, "Russian officials said they no longer disputed a damning set of facts that detailed a doping program with few, if any, historical precedents."
A "lab director tampered with urine samples at the Olympics and provided cocktails of performance-enhancing drugs, corrupting some of the world's most prestigious competitions. Members of the Federal Security Service, a successor to the KGB, broke into sample bottles holding urine. And a deputy sports minister for years ordered cover-ups of top athletes' use of banned substances," Ruiz wrote.
Antseliovich told CNN's Matthew Chance that Ruiz "changed" what she said, and Antseliovich denied admitting that doping in Russia was an institutional conspiracy.
It was actually lawyer Richard McLaren who used the word "institutional" in an interview with the Times, she told CNN.
The World Anti-Doping Agency
commissioned McLaren to investigate Russian doping allegations. Antseliovich said she merely welcomed the fact that his language had changed from "state sponsored."
"From the very start (of the doping scandal) we denied any involvement of the state, state agencies, services or bodies in the possible use of doping by athletes," Peskov told reporters Wednesday.
Hours after the Times story appeared, RUSADA issued a statement saying Antseliovich's comments were misrepresented.
"Unfortunately, [NYT reporter] Rebecca Ruiz has taken these words out of context creating an impression that RUSADA's top management admits an institutional scheme of covering doping in Russia," the agency said.
"We'd like to stress that RUSADA does not have and cannot have authority to admit or deny such facts. Russia's Investigative Committee is conducting an investigation into the matter," the statement added.
A 'systematic and centralized cover-up'
The New York Times story follows a report commissioned by the World Anti-Doping Agency
that claimed the Russian state conspired with athletes and sporting officials to undertake a doping program that was unprecedented in its scale and ambition.
A "systematic and centralized cover-up" benefited more than 1,000 Russian athletes across 30 sports, McLaren said in an update to the report first published in July.
"We know for sure it went to the Deputy Minister of Sport level -- beyond that we have no evidence to indicate that it went any further," McLaren told CNN.
The International Olympic Committee announced after the WADA report it would retest all 254 samples collected from Russian athletes who took part in the 2014 Winter Olympics in Sochi.
The Kremlin said it would study the report thoroughly, but will "refrain from forming an emotional response to allegations of the 'state conspiracy,'" according to state news agency Sputnik.
Russia's ministry for sport denied a state-sponsored program to aid doping in sports and stressed it is "continuing its fight against doping from the position of 'zero tolerance.'"
Evidence of doping found in Olympians' samples
In Sochi, two female ice hockey players' samples were found to contain male DNA
, while samples from two gold medalists and one female silver medalist were found to have "physiologically impossible salt readings," according to the WADA report.
Also, 44 of the samples examined -- including 12 from medal-winning athletes -- had scratches and marks on the caps of the bottles, indicating tampering.
Fifteen Russian medal-winning athletes from London 2012 were also found to have been involved in doping.
Russia won 72 medals at the 2012 London Games, 21 of which were gold. The country won 33 medals at the 2014 Sochi Games, 13 of which were gold.
"The Russian Olympic team corrupted the London games on an unprecedented scale -- the extent of which will probably never be fully established," the report said.
The scope of the subversion is "alarming," WADA President Sir Craig Reedie has said.
Previously, the IOC said the findings show a "fundamental attack on the integrity of the Olympic Games and on sport in general."
Following the WADA report, Russian parliament member Dmitry Svishchev said the accusations were "unsubstantiated," while politician Igor Lebedev said "there were no facts and no evidence."
The International Association of Athletics Federations (IAAF) has said it agreed with McLaren that "it is time that this manipulation stops" and says it is pursuing "a more specific, intelligence-based retesting program."
The International Paralympic Committee said the findings of the report were "unprecedented and astonishing."
"They strike right at the heart of the integrity and ethics of sport," the IPC said in a statement.
In November, Russian President Vladimir Putin signed a new law to criminalize any encouragement for doping, national news agency TASS reported.
Anyone found guilty of inducing an athlete to use drugs faces a fine of up to 1.1 million rubles ($11,400) or a jail term of up to three years, plus suspension from "professional activities" for up to five years, depending on the circumstances.
Following the initial report, WADA called for a blanket ban on Russian competitors at the 2016 Rio Olympic Games, but the International Olympic Committee ruled each sporting federation should decide whether Russians should be admitted.
Russia's track and field team and weightlifting squad were eventually excluded from the Games in August.
Official: Let's move on from doping scandal
In an interview with The New York Times, Vitaly Smirnov, the official Putin appointed to "reform the nation's antidoping system," said many athletes agreed to be doped to overcome preferential treatment that international authorities had given to athletes from Western nations.
"The general feeling in Russia is that we didn't have a chance," Smirnov told the Times.
While he publicly acknowledged the doping scandal, Smirnov expressed a desire to move on instead of blame people for what happened in the past, the Times report said.
"We have to find those reasons why young sportsmen are taking doping, why they agree to be doped," Smirnov said.
But Putin recently said at a news conference that claims about a state-run doping system were "absolutely impossible." He has vowed to take action on the broader problem of performance-enhancing substances.
"Like any other country, we have a doping problem," Putin said. "We must admit this, and by doing so, we must do everything in our power to prevent any doping."
The Kremlin now awaits the results of an investigation, Peskov added.