Speaking shortly after the International Association of Athletics Federations (IAAF) declined to lift a doping ban, Mutko said Russia had done everything it was asked to and added that the IAAF criteria were unclear.
"You say we should elect new leadership for the athletics federation - OK, we've done that. You should not elect anyone to be the leader who has done this or that - OK, we did that," he said in an interview at the Russian Sports Ministry.
"There are no criteria. What should Russian athletics do? Dance on the table? Sing a song?"
The IAAF said earlier on Friday Russia had "significant work to do" before it was reinstated, after a report by the World Anti-Doping Agency exposed widespread cheating and corruption in Russian athletics last year, igniting the country's biggest sporting scandal in decades.
IAAF president Sebastian Coe suggested a final decision would be taken in May, while Mutko said the "point of no return" for Russian athletes hoping to go to Rio was mid-July.
As things stand, Russian athletes will be barred from competing at this summer's Olympics, a humiliating blow to the reputation of a sports superpower where success is seen as integral to national pride.
Mutko said the IAAF's decision to uphold the ban would further punish athletes who are clean and also damage Russian competitors' performance in Rio if in the end they are allowed to compete at the Games.
"For another several months our teams will remain in a state of not knowing about what is going to happen," he said. "It means that our sportsmen will lose their competitive edge. It means that clean sportsmen will yet again be punished for nothing.
"This completely contradicts the spirit and philosophy of sport and the whole struggle against doping."
Russia has a proud history as a dominant force in world athletics and placed second behind the United States in the track and field medal table at the London Olympics in 2012.
But missing the Rio Games would result in funding being cut and push sponsors to look elsewhere, endangering the future of Russian athletics, Mutko said.
"If you want to stop the development of athletics on the territory of Russia, in the historical perspective, if you want to kill it - go on, kill it," he said.
(Editing by Hugh Lawson)
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