NEW YORK -- NFL Commissioner Roger Goodell and chief assistant Troy Vincent were told by 11 former players Tuesday that the league must act immediately when someone is accused of domestic violence.

At a 3 1/2-hour meeting to discuss ways to improve the league's personal conduct policy, the former players also said teams must be held accountable when players misbehave.

"One question asked around the room was, when an arrest occurs, do you take them off the field or let them play and let the due process take care of itself?" said Vincent, the NFL's vice-president of football operations. "To a man, they said, 'Take them off the field, pay them, and let due process take care of itself."'

At the meeting were Hall of Famer Mike Singletary, plus Matt Birk, Eddie Mason, Patrick Kerney, Willie McGinest, Roman Oben, Marty Lyons, Charles Way, Tony Paige, Scott Turner and Robert Porcher. More weekly meetings are planned among league officials and former players, current players and team owners.

"I felt like the clock was on after last Friday and the clock was on that we can't talk to enough people," Vincent said of a news conference at which Goodell announced the league will re-examine how and when it should discipline players for violating the policy.

"You begin this discussion with people it means the most to: the players and the owners," Vincent added. "Let's begin by bringing in some of our 'thought leaders."'

The NFL has faced heavy criticism of its personal conduct policy after incidents this year involving Ray Rice, Adrian Peterson, Greg Hardy, Ray McDonald and Jonathan Dwyer. Goodell repeatedly has said he mishandled the punishment of Rice for punching his then-fiancee in a hotel elevator.

Vincent said the meeting became emotional at times as the players stressed the importance of "making sure everyone is accountable."

Singletary, the great former Bears linebacker, pointed out the need to "find who is most influential person in this person's life" and then get the message across that if the player can't accept societal and league rules, "the lines are long behind them, and the people on those lines are ready to step up and assume the responsibility."

Vincent said he felt the league got a bit closer to finding solutions to swifter and more emphatic punishments for players who violate the personal conduct policy.

"You can't negotiate the game," Vincent said, his voice cracking. "The one thing we all got to fight for ... we are talking about the game and we all got to be all-in. We all have got to answer the questions of where are we today, how did we get here, why is this happening, how do we stop this and manage this?

"We don't have time to wait on anybody to give us direction. There is one thing we don't negotiate, it's the game."