With Russia enduring doping scandals for months, Mutko vowed to crack down on doping among child athletes, which he suggested was the result of a system where youth coaches can be paid sizeable bonuses when young athletes win competitions.
A holdover from the Soviet era, Russia has hundreds of children's sports academies spanning dozens of Summer and Winter Olympic sports.
While discussing ways to strengthen Russia's anti-doping enforcement, Mutko said "we will go down to children's sports schools to give a slap on the wrist to coaches who want to win some kind of championship at any price and get a bonus," in comments reported by R-Sport.
In cases of youth doping, "then the (athlete) gets into the national team and can't fulfil his potential," he added.
Mutko said Russia was pouring "colossal resources" into the fight against doping.
The World Anti-Doping Agency and the IAAF have each opened investigations into claims of systematic doping by Russian athletes, following the broadcast in December of a German TV documentary in which whistleblowers alleged drug use in Russian track and field, and the Russian national anti-doping agency covered up positive tests by leading Russian athletes.
Last month, athletics' world governing body said that since it introduced biological passports in 2009, more than half of all athletes banned under the testing system were Russians. So far this year, four Russian Olympic champions have been banned under the system, including 3,000-meter steeplechase winner Yulia Zaripova, who stands to lose her 2012 Olympic gold medal after being banned last Friday.
However, Mutko insisted Russia was not a world leader in doping, and that the percentage of its athletes caught using banned substances "is like in America, England, and all the other countries. The (anti-doping) system works."
Four top Russian race-walkers are under investigation by the IAAF over claims they broke the terms of their suspensions by competing at a Russian regional meet in December. They include Olympic champions Elena Lashmanova, currently banned for two years for doping, and Sergei Kirdyapkin, who was provisionally suspended at the time and received a ban last month. If they are found to have breached the terms of their suspensions, they could miss next year's Olympics.
Mutko said he believed that athletes had competed who "did not have the right to take part," but did not specify whether he thought Lashmanova and Kirdyapkin were among them. He suggested regional sports officials could be fired for allowing them to compete.