Russia is for the first time conceding that its officials carried out one of the biggest conspiracies in sports history: a far-reaching doping operation that implicated scores of Russian athletes, tainting not just the 2014 Winter Olympics in Sochi but also the entire Olympic movement.

Over several days of interviews here with The New York Times, Russian officials said they no longer disputed a damning set of facts that detailed a doping program with few, if any, historical precedents.

“It was an institutional conspiracy,” Anna Antseliovich, the acting director general of Russia’s national antidoping agency, said of years’ worth of cheating schemes, while emphasizing that the government’s top officials were not involved.

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 K.G.B., broke into sample bottles holding urine. And a deputy sports minister for years ordered cover-ups of top athletes’ use of banned substances.