Mikhail Mamiashvili had told local media there were "several tens" of doping cases in Russia, but later said he was not speaking only about wrestling.
"I meant the facts that have already been stated in speedskating, figure skating, swimming and other sports," he was quoted as saying by the Tass news agency.
Russian sports have been hit by several doping scandals in recent years. The recently banned endurance-boosting drug meldonium is responsible for a new wave of failed doping tests this year by Russian athletes, including Maria Sharapova.
Mamiashvili told Tass he was not aware of any other doping cases in Russian wrestling.
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In neighbouring Georgia, there have been six failed doping tests for meldonium in the country's national wrestling team, including Olympic silver medallist Davit Modzmanashvili.
He faces a possible life ban for a second career offense.
Russia finished at the top of the medals table in wrestling at the 2012 London Olympics and won seven gold medals at this month's European championships.
"Mutko will continue to work as the sports minister," Putin spokesman Dmitry Peskov said. "Let's not forget that the president ordered an in-depth investigation into the meldonium scandal. In this case, we need to reconstruct events to avoid this in the future.