Mutko said the appointment of Grigory Rodchenkov, who was behind the systematic violation of anti-doping rules in Russia, as the head of Moscow's anti-doping laboratory, had been approved by WADA.
"We've acknowledged that this man (Rodchenkov) himself violated all the WADA rules, regulations and standards," Mutko told R-Sport news agency. "And we've fired him.
"We are rearranging the (anti-doping) system but it should be rearranged so that WADA could also share responsibility. They should have been responsible for (Rodchenkov) before as they have issued him a licence and given him a work permit.
Mutko insisted that Russian authorities had never run a state-sponsored doping programme and pinned all the blame on the laboratory and Russia's Anti-Doping Agency (RUSADA).
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"It's necessary to put this story to rest and stop blaming the whole of Russian sport because we've been under the control of international sports organisations for two years," Mutko added.
WADA has accused Russian authorities of running a state- sponsored programme across sports to aid and protect drug cheats.
RUSADA was declared "non-compliant" with international sport's anti-doping code in November 2015 in the wake of the report by professor Richard McLaren which uncovered widespread doping in Russian sport.
Earlier this year WADA partially lifted RUSADA's ban, giving the agency the right to collect samples from doping tests.