"We urge you and the National Football League to send the same clear message as the NBA did," the senators wrote, adding it was the "opportunity for the NFL to take action to remove the racial slur from the name of one of its marquee franchises."
"What message does it send to punish slurs against African Americans while endorsing slurs against Native Americans?"
The letter said tribal organisations representing more than two million Native Americans across the US have said they want the Redskins name dropped.
Despite federal laws intended to protect tribal culture and identity, "every Sunday during football season, the Washington DC football team mocks their culture."
Senate Majority Leader Harry Reid and Senator Maria Cantwell, chairwoman of the Senate Indian affairs committee, led the letter-writing effort. Florida Democrat Bill Nelson wrote separately.
By Alan Fram
In one letter, 49 senators cited the NBA’s quick action recently to ban Los Angeles Clippers owner Donald Sterling for life after he was heard on an audio recording making offensive comments about blacks. They said Goodell should formally push to rename the team.
"We urge you and the National Football League to send the same clear message as the NBA did: that racism and bigotry have no place in professional sports," read the letter.
Sen. Bill Nelson, a Florida Democrat, wrote his own letter saying he doesn’t believe that retaining the Washington team name "is appropriate in this day and age." He described himself as "one of your great fans for both the game and you personally."
The letters come at a time of growing pressure to change the team name, with statements in recent months from President Barack Obama, lawmakers of both parties and civil rights groups.
NCAI Executive Director Jackie Pata said: "The name of Washington's NFL team is widely recognized as a racial slur. The NFL is a global brand, but if it wants to contribute to the positive image of the United States across the world, rather than callously promoting discrimination against Native Americans, then it must stop promoting this slur and finally change the name."
In recent months, the campaign to change the Washington NFL team name has received strong bipartisan support in Congress from advocates including House Minority Leader Nancy Pelosi, and Representatives Tom Cole, Betty McCollum and Eleanor Holmes Norton. In addition to federal legislators, policymakers at the state and local levels have also been critical of the Washington team's continued use of the R-word epithet. City councils, mayors, governors, and even the President of the United States have spoken out against the ongoing use of the slur.
Just days ago, the New York State Assembly unanimously passed a resolution calling upon professional sports leagues to end their use of racial slurs. The NFL is headquartered in New York, and the resolution specifically cites the Washington NFL team's R-word mascot as a dictionary-defined epithet.
Change the Mascot has also received support from civil rights organizations, faith leaders, sports icons, leading journalists, and top Native American organizations.