The charges were the latest involving the Olympics showcase sport, which scrapped its year-end gala on Friday after French officials began investigating the former president of athletics' ruling body for corruption.
It is the second global sporting federation to face allegations of corruption this year after the FIFA world football association.
TASS news agency said Russia's Lilya Shobukhova had previously told German broadcaster ARD she paid the Russian Athletics Federation 450,000 euros ($480,000) to be allowed to participate in the 2012 Olympic Games. Reuters was not able to reach Shobukhova for comment.
French investigative news organisation Mediapart said it had seen the conclusions of an independent investigation commissioned by the World Anti-Doping Agency (WADA) and that the inquiry exposed an extortion racket that targeted a Turkish athlete as well as six Russians, using an IAAF list of doping suspects as leverage.
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A WADA spokesman said on Saturday the agency would have no comment on the allegations or the report until the report is released on Monday. The International Association of Athletics Federations (IAAF) could not be reached for comment.
The federation's former chief Valentin Balakhnichev told told Russian news agencies the problems in international athletics were fuelled by political pressures, as was the corruption scandal surrounding FIFA.
"Let them present their claims to me, I will fight them," he was quoted as saying. "This is purely political."
TASS quoted Russian Sports Minister Vitaly Mutko as saying late on Friday: "Balakhnichev's case has been under consideration for a while ... It is difficult to say that the opening of a case against Balakhnichev is news."
The Russian Athletics Federation said on Friday it was aware of the WADA and IAAF investigation and prepared to cooperate, adding it "rejects any unfounded accusations against the organisation" and would "always act in accordance with international and domestic law, to realise its strategic partnership with the IAAF ... to represent and defend the interests of Russian athletics and Russian athletes."
Earlier this week Lamine Diack, former head of the Monaco-based IAAF, was put under formal judicial investigation with two other former IAAF officials by French magistrates who suspect them of corruption. Diack's family has dismissed what they called "excessive and insignificant accusations".
WADA plans a news conference on Monday in Geneva.
($1 = 0.9309 euros)
(Reporting by Brian Love; Editing by Jon Boyle and Ruth Pitchford)
