Russia has been barred from international track and field competition -- including the Rio Olympics -- since November 2015 following a damning report alleging state-sponsored doping in the country in Olympic sports over several years.
Moscow denies any state role in doping but Mutko, who was promoted from sports minister to deputy prime minister despite the doping controversy, pointed the finger at Russia's athletics coaches.
Russia's tainted athletics federation ARAF "had a lot of (doping) violations", he told the R-Sport agency.
On Monday world athletics boss Sebastian Coe said that Russia could not be reintegrated into the sport before November, meaning the country will miss August's world championships in London.
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The IAAF said Russian progress over doping was mixed, pointing also to "unhelpful public comments recently made by some Russian sporting officials" -- a possible reference to the outspoken Mutko, who is close to Russian President Vladimir Putin.
Mutko said that Russia -- which insists that drug cheating is an international issue -- was cleaning up its act.
"They (IAAF) tell us: you have done great work but there is still a lot to be done (to stop Russian doping).
"That happens when there aren't clear criteria, clear regulations."
ARAF deputy chief Andrei Silnov said he was buoyed by IAAF comments which said that while Russia was not ready to return to the fold, it recognised "several positive developments".
"They don't have any serious grudges against us," he told a press conference.
Individual Russian athletes can apply to take part in international events as neutrals if they are deemed drug-free.
"They said we have a chance to compete as neutrals but for some reason we still do not compete," he said.
Sports minister Pavel Kolobkov told TASS news agency that if any Russian athletes qualify as neutrals then Moscow would guarantee funding.
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