(CNN) -- The National Football League announced Monday it will not overturn the penalty it previously imposed against the New Orleans Saints and members of its coaching staff for the team's bounty program. NFL Commissioner Roger Goodell did not alter the lengths of the suspensions he had levied last month. But he left open the possibility that fine amounts could be reduced and a draft pick could be restored if the team and its coaching staff "embrace the opportunity" to help develop and implement player safety programs. The unprecedented punishment was handed down in March after an NFL investigation found the team had an "active bounty program" during the 2009, 2010 and 2011 seasons. During this time, players were purportedly offered "bounty" payments if they managed to hurt opposing players and knock them out of a game.
@highlight
NEW: After the suspensions' end, the commissioner will "review" the cases
@highlight
NEW: Payton's suspension starts April 16, the GM's starts late this summer
@highlight
They had appealed the suspensions handed out last month
@highlight
The NFL says Saints players were offered extra money to hurt opposing players
In public remarks, @placeholder has not admitted he lied to the NFL and insisted that no one was injured as a result of the bounty program.