Alexei Sorokin, the committee’s chief executive, will take on Mutko’s responsibilities, another agency, TASS, cited Mutko as saying, Reuters reports.
“He (Sorokin) will interact with FIFA. I will coordinate the work on the government side,” Mutko told TASS.
Russia is hosting next year’s soccer World Cup in 11 cities including Moscow, St Petersburg and Sochi.
But Mutko, a former sports minister, has been embroiled in a scandal concerning alleged doping at the 2014 Sochi Winter Olympics in Russia.
Read alsoRussian team suspended from Pyeongchang Winter Games, clean athletes may compete under Olympic flagThe International Olympic Committee said this month it was banning Russia from the 2018 Pyeongchang Winter Olympics after finding evidence of “unprecedented systematic manipulation” of doping procedures.
Mutko says there was no state-backed doping program.
Mutko said earlier this week that he was temporarily stepping down from his role as head of the country’s Football Union.