"We are of course pleased with the results on the whole. Russia supported Blatter," Mutko told RIA Novosti state news agency.
"As members of the European family, we consider that it's necessary to draw serious conclusions, to do everything to make changes happen (in FIFA)," Mutko added.
Swiss police on Wednesday detained several FIFA leaders accused by US authorities of taking tens of millions of dollars in bribes.
Swiss police are also investigating the awarding of the 2018 and 2022 World Cups to Russia and Qatar which have also been surrounded by corruption allegations.
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Putin claimed that Blatter has previously rejected "pressure put on him with the aim of banning" Russia from hosting the 2018 World Cup.
The investigation into the FIFA corruption scandal plans to question 10 members of its executive committee who took part in the vote awarding the World Cups to Russia in 2018 and Qatar in 2022.
Mutko was on the committee although it is not clear whether he is one of the people to be questioned.