They suggested that FIFA hold an extraordinary congress to vote on whether to move the 2018 tournament to another site.
According to the letter, more than 40 countries, including nearly half of the field from the 2014 World Cup, have placed sanctions on Russia. Keeping the World Cup there in three years "provides economic relief," the letter added.
"As you know, nearly a full year has passed since unmarked Russian troops and Russian-backed separatists began their dismemberment of Ukraine," the Senators said.
They explained they wrote "with the goal of ending the crisis in Ukraine and ensuring a successful 2018 World Cup."
Asked to comment on the letter, FIFA spokeswoman Delia Fischer rejected the notion that it makes sense to strip Russia of the World Cup.
"History has shown so far that boycotting sport events or a policy of isolation or confrontation are not the most effective ways to solve problems," Fischer wrote Wednesday in an email to The Associated Press, adding that hosting the World Cup "can be a powerful catalyst for constructive dialogue between people and governments, helping to bring positive social developments."
Fischer also wrote that FIFA believes it "can achieve positive change in the world, but football cannot be seen as a solution for all issues, particularly those related to world politics."
"We have seen that the FIFA World Cup can be a force for good," she said, "and FIFA believes this will be the case for the 2018 FIFA World Cup in Russia."
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