"Hopefully, it will become a kind of a conciliating event, which will show the world that Russia is an open-hearted, democratic and hospitable country with a rich history and culture," Mutko told R-sport agency.
"It will be a great occasion not only for Russia but for the entire football world," said Mutko.
Relations between Russia and the West have been tense since the annexation of Crimea in March last year and an ensuing conflict in Ukraine that has claimed more than 8,000 lives.
There is also bitterness amongst other 2018 candidates over allegations Russia was awarded the rights to host the World Cup after a deal with FIFA was apparently agreed in advance.
2018 World Cup: Blatter claims hosts chosen before vote
Russia's cold war rivals Britain are angry with the 2018 World Cup going to Russia while the United States are also uncomfortable with the 2022 World Cup going to Qatar.
Mutko also said Russia was fulfilling its commitments towards FIFA deadlines on World Cup infrastructure perpetrations despite the economic crisis.
"We're doing our best to develop our facilities and to urge the development of football in the country," he said.
"I don't see any really outstanding problems.
"Despite the complicated economic situation we have managed to keep to our World Cup investment budget. It will help Russia to fulfil all of its obligations in full."
FIFA has approved 62 of the 64 training bases to be used by teams' for accommodation and practice during the tournament, Mutko confirmed.
He also revealed that representatives of certain teams had already visited some of the bases first presented at the preliminary draw ceremony earlier this year.
"The representatives of Germany, Netherlands, England, Brazil, USA, Mexico and some other event favourites have already visited the training bases this year and gave them a positive rating," the minister said.
The 2018 World Cup will take place at 12 venues across Russia betwwen June 14 - July 15 2018.
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