By a 10-0 vote, the council approved a resolution Tuesday urging the team to abandon the nickname, which some consider offensive to Native Americans. One member abstained, and two were absent.
The council has no power over the team, which plays its home games in Maryland and has its training facility in Virginia. It previously called for a name change in 2001.
President Barack Obama said recently that he would consider changing the name if he owned the team. Redskins owner Daniel Snyder has called the name "a badge of honour" but says he respects the feelings of those who are offended.