Among the other recommendations, WADA said worldwide federations from sports implicated in the report consider action against Russian national bodies and that Mr McLaren and his team complete their mandate provided WADA can secure funding.
Rodchenkov, who was sacked after the first WADA-funded investigation into doping in Russian athletics past year, has been in hiding in the United States ever since and has been branded a "criminal" and a "traitor" by senior Russian figures.
But he did not make any recommendations for the future of the Russian team, saying it was up to others, including the International Olympic Committee, to "absorb and act upon" the 97-page report.
He claimed that up to 15 Russian medal winners at the Sochi Winter Games were part of a programme in which tainted urine samples were switched for clean ones.
He said the 312 results that were held back represented only a "small slice" of the data that could have been examined.
However, FIFA did not comment directly on allegations in the World Anti-Doping Agency (WADA) report that Russian Sports Minister Vitaly Mutko, who sits on its supervisory FIFA Council, had ordered the cover-up in the cases of the footballers.
The International Olympic Committee had previously said it could impose tough new sanctions against Russian Federation over the Rio 2016 Games.
A Wada statement said: "Given that the Russian Ministry of Sport orchestrated systematic cheating of Russian athletes to subvert the doping-control process; and that the evidence shows such subversion in 30 sports, the presumption of innocence of athletes in all Russian sports is seriously called into question".
Russia's athletes should fear the worst, as the World Anti-Doping Agency urged the International Olympic Committee to ban Russian Federation from the Olympics altogether.
McLaren said Rodchenkov and all other witnesses interviewed had been deemed credible, and the report said the investigators "confirm the general veracity of the published information concerning the sample swapping that went on at the Sochi Laboratory during the Sochi Games".
Vladimir Putin said the latest report on doping among Russian athletes lacked substance and was highly political.
Travis Tygart, the CEO of USADA, urged the worldwide community to come together to ensure that what he called an unprecedented level of criminality never threatens sports again.
The British Olympic Association said the report "realises the worst fears of clean athletes everywhere", while UK Anti-Doping urged the sports community to "come together" and safeguard clean athletes.
Members recommended that the International Olympic Committee (IOC) take immediate action to stop Russian athletes from competing in next month's Olympics, especially since the report underscores WADA's own findings. "It enable Russian athletes to compete dirty while being certain that their samples would be reported clean".
The focus of the investigation was on the Sochi 2014 Winter Olympics but also included claims about a number of summer Olympic sports.
He was relying on the IOC and global sports federations to figure out appropriate sanctions. But despite WADA's recommendation, there is far from a consensus on what those sanctions will be, as the sports world toes the line between what Bach called "collective responsibility and individual justice".
That urgent verdict is scheduled for Thursday but could be rendered meaningless by an International Olympic Committee blanket ban.