Rodchenkov claimed an instruction to "avoid any scandal" came from Mutko, ensuring that "Russian footballers were immune from doping-control actions or sanctions."
While Mutko has been banned for life from the Olympics, he has not faced any footballing sanctions.
"When they (Russian footballers) had AAFs those results were supposed to stay out of ADAMS," Rodchenkov said, referring to adverse analytical findings not being logged in the World Anti-Doping Agency's administration and management system.
Russia has denied there was a state-sponsored doping system but Mutko said last month that national team player Ruslan Kambolov, a defender at Rubin Kazan, was one of two Russian players already embroiled in a FIFA doping investigation.
Although Rodchenkov oversaw the destruction of around 8,000 doping controls in 2014 when the state-backed scheme was exposed, WADA managed to seize 3,000 samples. Forensic checks have just started on 154 samples from footballers to detect any manipulation of the samples, including scratch marks which could prove that bottles were forced open and tainted urine swapped out.
FIFA medical committee chairman Michel D'Hooghe said he "cannot say" if the analysis would be completed before Russia opens the World Cup against Saudi Arabia.
"That depends on WADA. That depends on the laboratories," D'Hooghe told the AP last week. "We are collaborating in all that we can to find the truth about what is happening in the world of football. ... I know if there is proof of a positive case that our disciplinary committee will take action."
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Rob Harris is at www.twitter.com/RobHarris and www.facebook.com/RobHarrisReports
AP World Cup coverage: www.apnews.com/tag/WorldCup