"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 St. Louis, 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 3 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.
Smith played in each of the Saints' first two games. 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.
In other NFL news:
* Washington defensive starters Brian Orakpo and Adam Carriker were declared out for the season. Two-time Pro Bowl linebacker Orakpo tore the pectoral muscle near his left shoulder, and defensive end Carriker tore up his right knee in Sunday's loss to St. Louis.
* Tackle David Diehl, running back Ahmad Bradshaw and wide receiver Domenik Hixon were among six Giants held out of practice on Monday. Diehl suffered an injury to the medial collateral ligament in his right knee in Sunday's win over Tampa Bay and might be the most questionable player for the Giants' next game, Thursday against Carolina.
* New England coach Bill Belichick says he doesn't know how long tight end Aaron Hernandez will be sidelined with a right ankle injury. ESPN.com reported that Hernandez would not play Sunday night at Baltimore and that, while there is no exact timetable, he likely will not return until October at the earliest.
* Cleveland tight end Alex Smith was briefly hospitalized with a concussion following Sunday's loss in Cincinnati. Rookie defensive tackle Billy Winn also suffered a concussion, and defensive tackle Juqua Parker sprained a foot.
* St. Louis tackle Rodger Saffold will be out at least a month because of a right knee injury. He was a surprise starter against Washington after being hospitalized with a neck strain in Detroit after the opener.
Coach Jeff Fisher dispelled rumors that running back Steven Jackson had been benched for spiking the ball in protest after he was ruled short of the goal line on a third-down carry from the 1, saying Jackson was held out with a minor groin injury.
In a game Monday *
At Atlanta, Penn Charter's Matt Ryan threw the 100th touchdown pass of his career and the Falcons (2-0) held off a fierce Peyton Manning comeback for a 27-21 victory over Denver. Manning was intercepted three times in the first quarter, but engineered two fourth-quarter touchdown drives and the Broncos made it close.