The Washington Redskins had a bounty system during the mid-2000s that rewarded players with thousands of dollars for big hits that knocked opponents out of games, a former Redskins coach and five players said Friday.

The program, which was operated under former defensive coordinator Gregg Williams between 2004 and 2007, was similar to one revealed Friday in a National Football League investigation of the New Orleans Saints while Williams was the defensive coordinator there.

Four of the Redskins players described an informal system under which Williams doled out thousands of dollars to Redskins defenders who measured up to his standards for rugged play, including for what one described as “kill shots” that sent opposing teams’ stars to the sideline.

“You got compensated more for a kill shot than you did other hits,” said one former Redskins player, who spoke on condition of anonymity.

The former coach, who was an assistant to Williams, said the defensive coordinator would reveal the amount of bounty money available to players as “a little extra incentive.” He said Williams would set the amounts in meetings before big games.

“It was a motivational tool, just like anything you would try to do as a coach to get the most out of players,” the former coach said. “The only thing was, money was involved.”

Players said such compensation, which is against NFL rules, ranged from “hundreds to thousands of dollars,” with the largest sum paid to any player believed to be about $8,000.

“I never took it for anything [but] just incentive to make good, hard plays,” said a current Redskins player, who requested anonymity. “But I’m pretty sure it did entice some guys to do more to a player than normal when it came to taking them out. I mean, that’s cash. Let’s just be honest about it.

“If you took the star player out, he’d hook you up a little bit.”

The revelations came during a period in which the NFL has tightened enforcement of rules and heavily fined violators as part of a campaign to protect players’ safety, particularly from head injuries.

Greg Aiello, the NFL’s senior vice president of communications, said the league was not aware of allegations of a Redskins bounty program under Williams. “No such information came forth in this investigation” of the Saints, Aiello said. He did not comment further.

The Redskins declined to comment through team spokesman Tony Wyllie.

Joe Gibbs, who was head coach during Williams’s tenure in Washington, said he was unaware of the bounty program and would have stopped it if he had known.

“Just let me say this: I’m not aware of anything like this when I was coaching there,” Gibbs said in a telephone interview. “I would never ask a player to hurt another player. Never.”

Of the five Redskins players interviewed, only Phillip Daniels, a former defensive lineman, was willing to be quoted by name. He defended Williams’s coaching.

Daniels, now the Redskins’ director of player development, said he believed Williams began the program with fines collected from players for being late for meetings or practices. “Rather than pocket that money or whatever, he would redistribute it to players who had good games or good practices,” Daniels said.

He said the most he ever received was $1,500 for a four-sack game against the Dallas Cowboys in 2005.

“I think it is wrong the way they’re trying to paint” Williams, Daniels added. “He never told us to go out there and break a guy’s neck or break a guy’s leg. It was all in the context of a good, hard football.”

He acknowledged Williams’s system for awarding players’ cash featured more money for what Williams deemed “physical play.”

“Sean Taylor made a lot,” he said of the hard-hitting safety who was slain in his Miami home in 2007.

The NFL announced Friday that the Saints operated an improper bounty program from 2009 to 2011 that included payments of as much as $1,500 for hits that injured opposing players.

Administered by Williams, now the defensive coordinator for the St. Louis Rams, the Saints’ bounty program paid $1,500 for a “knockout” hit and $1,000 if an opponent was carted off the field, the NFL said. Most of the money was contributed by players, but Williams also donated to the fund, according to the league.

Williams issued an apology about the Saints’ bounty program Friday.

“I want to express my sincere regret and apology to the NFL, [Saints owner Tom] Benson, and the New Orleans Saints fans for my participation in the ‘pay for performance’ program while I was with the Saints,” he said. “It was a terrible mistake, and we knew it was wrong while we were doing it. Instead of getting caught up in it, I should have stopped it. I take full responsibility for my role.”

Between 22 and 27 players participated in the Saints’ bounty program, the NFL said. Coach Sean Payton was not a direct participant but was “aware of the allegations” and “failed to stop the bounty program,” according to the league. Benson ordered Saints General Manager Mickey Loomis to halt it, but Loomis did not comply, the investigation found.

NFL Commissioner Roger Goodell will determine disciplinary action that, according to the NFL, could include fines, suspensions and the forfeiture of draft choices by the Saints.

“The payments here are particularly troubling because they involved not just payments for ‘performance,’ but also for injuring opposing players,” Goodell said in a written statement released by the league. “The bounty rule promotes two key elements of NFL football: player safety and competitive integrity.

“It is our responsibility to protect player safety and the integrity of our game, and this type of conduct will not be tolerated.”

Benson pledged the Saints’ full cooperation in the NFL’s investigation. “While the findings may be troubling, we look forward to putting this behind us and winning more championships in the future for our fans,” he said.

Goodell said the investigation began in early 2010 when the NFL first heard claims that Saints players had targeted opposing players, including Cardinals quarterback Kurt Warner and Vikings quarterback Brett Favre.

“Our security department interviewed numerous players and other individuals,”Goodell said. “At the time, those interviewed denied that any such program existed and the player that made the allegation retracted his earlier assertions. As a result, the allegations could not be proven.

“We recently received significant and credible new information and the investigation was reopened during the latter part of the 2011 season.”

The four Redskins players who spoke on condition of anonymity portrayed Williams as a “coach who just took it a little too far,” in the words of one.

“He actually had a saying, ‘If you cut the snake’s head off, the body will die.’ That was his motto,” the player said. “It was made clear that he was talking about not just running backs who turned their heads the opposite way and how they would go down, but also about other stars on offense that were the best players on that team.”

The former Redskins coach said “you have to understand that with the money guys make now, it’s not as much of an incentive like it used to be. Also, with Facebook and Twitter and everything, guys are much friendlier than they were years ago.

“Everyone knows each other, so guys aren’t going to go out there and try to hurt people. It’s just not the way it used to be. The [bonus] money just doesn’t mean as much. It used to be that guys would go out there and try to kill each other for a three-piece Popeyes meal.”

Staff writers Mike Wise, Jason Reid and Mike Jones contributed to this report.