Published: Jul 03, 2012 9:41 PM EDT
Updated: Jul 04, 2012 6:31 AM EDT

NEW ORLEANS (AP) - NFL Commissioner Roger Goodell has rejected the appeals of four players suspended in connection with the league's bounty investigation of the New Orleans Saints.

In a ruling handed down on Tuesday, Goodell told Jonathan Vilma, Anthony Hargrove, Will Smith and Scott Fujita that he retains "the inherent authority to reduce a suspension should facts be brought to my attention warranting the exercise of that discretion.

"The record confirms that each of you was given multiple chances to meet with me to present your side of the story," Goodell said. "You are each still welcome to do so."

Vilma is suspended for the entire 2012 season, while Smith will miss four games. Hargrove, now with Green Bay, was suspended eight games, while Fujita, now with Cleveland, was suspended three games.

The NFL Players Association issued a statement saying it will continue to pursue all options.

"The players are disappointed with the League's conduct during this process," the statement said. "We reiterate our concerns about the lack of fair due process, lack of integrity of the investigation and lack of the jurisdictional authority to impose discipline under the collective bargaining agreement.

"Moreover, the Commissioner took actions during this process that rendered it impossible for him to be an impartial arbitrator."

Goodell said he did not take his initial decision lightly and also points out that players did not help their cause by refusing to participate fully in the appeal process.

Vilma and his attorney, Peter Ginsberg, walked out of the hearing early after Ginsberg raised his objections to the NFL's handling of the entire investigation. The other three players, who were represented by NFL Players Association attorneys, sat through the hearing to observe the NFL's presentation of evidence, but in protest refused to present any evidence or witnesses of their own, and did not question the NFL investigators who were present at the hearing.

"Although you claimed to have been 'wrongfully accused with insufficient evidence,' your lawyers elected not to ask a single question of the principal investigators, both of whom were present at the hearing," Goodell wrote in his appeal ruling. "You elected not to testify or to make any substantive statement, written or oral, in support of your appeal; you elected not to call a single witness to support your appeal; and you elected not to introduce a single exhibit addressing the merits of your appeal. Instead, your lawyers raised a series of jurisdictional and procedural objections that generally ignore" the collective bargaining agreement.

The NFL issued a report in March saying that league investigators determined the Saints ran a bounty program from 2009 to 2011 that offered improper cash payments for hits that injured targeted opponents.

The league has said former Saints defensive coordinator Gregg Williams ran the program, and that general manager Mickey Loomis and head coach Sean Payton failed to put a stop to it despite warnings from the NFL at the end of the 2009 season.

The NFL has suspended Williams indefinitely and Payton for the whole season. Loomis is suspended the first half of next season, while Saints assistant head coach Joe Vitt was suspended for the first six games. Goodell also docked the Saints second-round draft picks this year and next and fined the club $500,000.