(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.
The NFL found evidence that bounties were put on quarterbacks Brett Favre of the Minnesota Vikings, Cam Newton of the Carolina Panthers, Aaron Rodgers of the Green Bay Packers and Kurt Warner of the Arizona Cardinals.
The stiffest penalty that the NFL handed down -- an indefinite ban -- was given to Gregg Williams, the Saints defensive coordinator who, in this past offseason, moved over to take that same position with the St. Louis Rams.
Head coach Sean Payton suspension for the entire 2012-2013 season will begin April 16, the league said Monday.
General manager Mickey Loomis was suspended without pay for that season's first eight regular-season games, and assistant head coach Joe Vitt was suspended without pay for the first six regular-season games. Their suspensions will begin at the end of the preseason, according to Monday's NFL statement.
"At the conclusion of their suspensions, the commissioner will review the status of each of the three individuals to determine their eligibility for reinstatement," the league said, referring to Payton, Loomis and Vitt.
The team was also fined $500,000 and ordered to forfeit its second-round draft picks in 2012 and 2013, the NFL has said. The league added Monday that it may consider "modifying the forfeiture" of the 2013 draft pick, assuming other conditions are met.
Goodell has said he's also considering imposing penalties against players involved in the bounty program, but he hasn't given a timetable and has insisted he'll first consult with the NFL Players Association before doing so.
In its ruling, the NFL singled out Payton -- who led the Saints to its first ever Super Bowl victory in February 2010, after a season in which the bounty program was in place -- by saying that violations for the bounty program "were compounded by the failure of Coach Payton to supervise the players and coaches."
The league said that Payton didn't look further into the "pay-for-performance/bounty program" despite the NFL's inquiries about it in 2010 and 2012, "falsely (denied) that the program existed" and encouraged "the false denials by instructing assistants to 'make sure our ducks are in a row.'"
In public remarks, Payton has not admitted he lied to the NFL and insisted that no one was injured as a result of the bounty program.
But he did say in late March, shortly after his suspension was announced, that he was "disappointed" in himself and regretted not being more involved in the team's defense.
"As the head coach, anything that happens within the framework of your team and your program you're responsible for. And that's a lesson I've learned," he said.