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 each of them is still welcome to meet with him to give their side of the story, and that he reserves the right to reduce the suspensions should new information be brought forth.

Instead, however, the players intend to fight Goodell's rulings through the federal court system.

The players have declined to meet with Goodell because they have argued that Goodell lacked the jurisdiction to rule in the matter and has violated the spirit of the league's Collective Bargaining Agreement by making public statements about the case that demonstrated he could not be a neutral arbitrator.

The players likely would have relinquished those legal arguments had they met with the commissioner to defend themselves through the NFL's regular disciplinary process.

Vilma, who was suspended for the entire 2012 season, has already filed two separate lawsuits in the matter in federal court in New Orleans. One is a defamation lawsuit against Goodell himself. The other, which named the NFL as a defendant, asks for a temporary injunction that would allow Vilma to continue working while other related legal matters play out.

The NFL Players Association also hinted at legal action on Tuesday, saying in a written statement that it ''will continue to pursue all options.''

''The players are disappointed with the league's conduct during this process,'' the union's 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.