Vilma met with Commissioner Roger Goodell on Monday in New York about his suspension, which has been temporarily lifted. Attorney Peter Ginsberg said they were given an affidavit at the meeting.
"What Gregg Williams said in his most recent affidavit is the same falsity he has previously provided," Ginsberg said.
"I don't know what Gregg Williams' motives are, but I do know that any suggestion by Williams that Jonathan put up $10,000 as an incentive for his teammates to injure another player is absolutely false."
Vilma tweeted on Monday night that Williams was "bullied to sign the affidavit," saying Williams signed it on Friday.
Williams is now with the St. Louis Rams, though he has been suspended indefinitely. An associate of his said Williams did not want to talk to the media.
Vilma, who denied in court that he offered money in exchange for injuring the former Vikings quarterback, was one of four players suspended by Goodell in the bounty scandal.
"Today everyone was afforded an opportunity to start over," Vilma said outside the NFL's Park Avenue offices more than three hours after he went in. "It was in our best interest to meet today. We spoke truthfully, honestly, bluntly."
An appeals panel earlier this month said Goodell must clarify his rulings to ensure no part of his decisions was based on salary cap violations. That would be the jurisdiction of special master Stephen Burbank.
Goodell must show that the basis for the discipline was inappropriate conduct — such as intent to injure — rather than any secret monetary compensation. In that case, he has full authority to impose the suspensions.
Players and coaches implicated in the bounty pool have testified under oath in a related federal court case they never intended to injure opposing players.
New Orleans defensive end Will Smith (four games), Browns linebacker Scott Fujita (three) and free agent defensive end Anthony Hargrove (eight) are expected to have their meeting Tuesday.
"We appreciate Jonathan Vilma taking the time to meet today and look forward to seeing the other players tomorrow," NFL spokesman Greg Aiello said.
Smith played in each of the Saints' first two games and Vilma is on the physically unable to perform list. Fujita made his season debut in Cleveland's loss to Cincinnati on Sunday. Hargrove was cut by Green Bay during the preseason.
Vilma, initially suspended for the entire season, requested a separate meeting. He hasn't played because he is on the physically unable to perform list as he rehabilitates following offseason surgery on his left knee.
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