An investigation by Canadian law professor Richard McLaren for WADA found the FSB secret service helped "the state-dictated failsafe system" carried out by the sports ministry and covering 30 sports.
"WADA calls on sport movement to deny Russian athletes participation at international competition including Rio until 'culture change' achieved," the international anti-doping agency spokesman Ben Nichols said in a statement on Twitter.
International Olympic Committee members were to hold an emergency telephone conference on Tuesday to decide provisional sanctions over what IOC president Thomas Bach called "a shocking and unprecedented attack on the integrity of sports and on the Olympic Games."
President Vladimir Putin made the Sochi Games a showcase event and more than $50 billion was spent putting it on.
Russia, which had strongly denied any state involvement, is already banned from international athletics by the world body, the IAAF, because of doping exposed last year.
There will no be mounting pressure for that to be extended even though Bach and some international federations have said there has to be a way for athletes proved to be clean to compete in Rio.
"The Moscow laboratory operated for the protection of
doped Russian athletes within a state-dictated failsafe system," McLaren said.
"The Sochi laboratory operated a unique sample swapping methodology to enable doped Russian athletes to compete at the Winter Olympic Games," he added.
McLaren did not make any recommendations on sanctions. But the call by WADA is likely to followed up by the United States and Canadian anti-doping agencies.
Both had said before the report's release that a blanket ban on Russia from Rio, which starts August 5, should be considered if the evidence was damning.
WADA mandated McLaren to investigate allegations made by former Moscow anti-doping laboratory director Grigory Rodchenkov in May.
Rodchenkov is now in hiding in the United States and wanted by Russian authorities. McLaren called the Rodchenkov "a credible and truthful person" despite admitting to concocting doping cocktails for Russian athletes.
"I realize there are other aspects of his life that are not appropriate," McLaren said. "I didn't need to get into that."
"I'm supremely confident in our findings," McLaren said. "We've had a very intense 57 days."
McLaren said his report was handed over to WADA on Saturday and had not been leaked in advance.
He said a US-Canadian letter pushing for a total ban on Russian competitors at Rio was based on "rampant speculation" about the findings.
"I don't think it has any impact whatsoever on the report and I pay no attention to it," McLaren said. "I'm positive the report was not leaked. What others did was all speculation.
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