First imposed in November, the IAAF ban was extended on Friday and supported by the International Olympic Committee (IOC) on Saturday.
"I have written an open letter to (the IAAF)... If you are an organisation whose aim is to develop athletics then you have done everything to destroy it," Vitaly Mutko told Reuters in an interview.
Russian track and field athletes had not participated in international competitions in January.
"I, on behalf of the state, cannot finance the country's national team. That means all this is falling apart. Next, I cannot finance the training centre, all these are closing down. The young athletes do not have any motivation," Mutko said.
Individual Russian track and field athletes assessed as clean will be able to compete for their country in Brazil, IOC President Thomas Bach said on Tuesday, diluting the IAAF's ban.
Mutko, turning to Russia's poor showing at the Euro 2016 soccer championships in France -- where the team failed to get beyond the group stage -- said he would like coach Leonid Slutski -- who has expressed a wish to step down -- to continue in his role.
"I would like him to continue working, but this is a question for him. We have discussed the outcome of the championship in great detail," Mutko said.
"I will give him a break of a few days, and will speak to him once again."
Slutski, who is also head coach of Russian champions CSKA Moscow, replaced Italian Fabio Capello in August 2015 and revived a team that had looked in danger of failing to qualify.
(Reporting by Parniyan Zemaryalai and Mikhail Antonov, writing by Vladimir Soldatkin; editing by John Stonestreet)
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