New Orleans Saints Coach Sean Payton and General Manager Mickey Loomis acknowledged responsibility Tuesday for violating NFL rules by allowing bounty payments to defensive players for jarring hits aimed at knocking opponents out of games over the past three seasons.

“We acknowledge that the violations disclosed by the NFL during their investigation of our club happened under our watch,” Payton and Loomis said in a written statement released by the Saints that was the pair’s first response to the results of an investigation released Friday. “We take full responsibility.”

Payton, Loomis, former Saints defensive coordinator Gregg Williams and players who were heavily involved in the bounty payments face possibly lengthy suspensions by NFL Commissioner Roger Goodell, a person familiar with the case said over the weekend.

Players and one former coach have said that the Washington Redskins had a similar bounty system for big hits under Williams when he was defensive coordinator from 2004 to 2007.

In an announcement Friday, the league cleared Saints owner Tom Benson of culpability in the bounties but cited Payton and Loomis for failing to take action to halt the program, which, the NFL concluded, was administered by Williams. The bounties were funded primarily by players, according to the league’s announcement Friday.

Benson at least once directed Loomis to halt the program but Loomis did not comply, the NFL concluded.

“This has brought undue hardship on Mr. Benson, who had nothing to do with this activity,” Payton and Loomis said in their statement. “He has been nothing but supportive and for that we both apologize to him.

“These are serious violations and we understand the negative impact it has had on our game. Both of us have made it clear within our organization that this will never happen again, and make that same promise to the NFL and most importantly to all of our fans.”