The council passed a similar resolution in 2001, and the new one has broad support on the 13-member body. It comes amid a national debate about the name, which some consider to be offensive to Native Americans. President Barack Obama recently said he would "think about changing" the name if he owned the team.
The resolution no longer suggests a new nickname for the team. Councilmember David Grosso (GRAH'-so), who wrote the original resolution, had suggested "Redtails" in honor of the Tuskegee Airmen.
The council has no power over the Redskins.
Representatives of the Oneida Indian Nation have requested a meeting with all 32 NFL owners during Super Bowl week to discuss changing the nickname.