Mutko, who is also a FIFA executive committee member and is in Zurich for the governing body's congress and presidential election, played a leading role in Russia's bid and said his country welcomes the investigation.
"We're prepared to show everything," Mutko said in a telephone interview to The Associated Press. "We've always acted within the law. We've got nothing to hide."
Swiss authorities said they are investigating the awarding of the 2018 World Cup to Russia and the 2022 tournament to Qatar. In a separate US investigation, 14 people were indicted on corruption charges and seven of them were arrested in Zurich.
"How can it be obstructed? ... We have a contract with FIFA and we're getting ready to hold the draw," Mutko said. "We operated within the regulations that existed at that time."
More From This Section
Alexei Sorokin, who headed Russia's bid committee and now runs the organizing committee, also said there had been no wrongdoing.
"We have stated that many times during the investigation by FIFA and before that investigation," Sorokin said by telephone from Zurich. "Preparations to host the World Cup are continuing and they are going according to plan."
Both Sorokin and Mutko said that they had not been contacted by investigators in connection with today's developments.