The federation's deputy president, Roman Rotenberg, told TASS news agency that the 2024 and 2025 world championships will be held in the Czech Republic and Sweden, respectively.
The International Ice Hockey Federation (IIHF) could not immediately be reached for comment.
Russian businessman Gennady Timchenko, an ally of President Vladimir Putin who serves as president of Kontinental Hockey League (KHL) club SKA St Petersburg, said last month he wanted to build the world's biggest hockey arena with a capacity of more than 22,000 seats.
The new venue, he said, could host the 2023 world championship.
The Russian men's team won gold at the Pyeongchang Games in February, ending a 16-year medal drought.
(Reporting by Gabrielle Tétrault-Farber, editing by Ed Osmond)
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