In the letter, the lawmakers argue that "Native Americans throughout the country consider the R-word a racial, derogatory slur akin to the N-word among African Americans or the W-word among Latinos."
"It also diminishes feelings of community worth among the Native American tribes and dampens the aspirations of their people," the group writes.
Earlier this year, a group of House Democrats introduced a bill that would prevent the term "Redskins" from being trademarked, a move intended to put pressure on the organization to change the name.
Snyder told USA Today earlier this month he has no plans to change the team's name.
"We'll never change the name," he said. "It's that simple. Never — you can use caps."