NEW ORLEANS — 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.

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

The NFL says its investigation found that Saints players paid into a system, run by former defensive coordinator Gregg Williams from 2009 to 2011, that offered improper cash payments to teammates who injured targeted opponents.

Vilma and Smith, who is suspended four games, are still with the Saints. Hargrove, now with Green Bay, was suspended eight games, while Fujita, who joined Cleveland in 2010, was suspended three games. Only Vilma’s suspension is effective immediately, while the other three players are able to participate in training camp.

Because Vilma is rehabilitating a left knee injury at the Saints’ training headquarters, he is seeking a quick ruling on his request in federal court for a temporary injunction.

Vilma’s attorney, Peter Ginsburg, did not immediately respond to a request for comment on Goodell’s latest ruling.

Fujita, a member of the NFLPA’s executive committee, said he was not surprised by Goodell’s decision, but that he still hoped for “a process that leads to a fair resolution and gets whole truth on the table.”

Fujita has called the bounty probe a “smear campaign,” and all four punished players have denied paying teammates to injure opponents.

So far, the NFLPA already has challenged Goodell’s authority to hear player appeals before two system arbitrators, who both ruled in favor of Goodell, citing language in the league’s labor agreement that gives the commissioner that authority.

Now the union must try to convince a federal judge otherwise.

The NFL has said more than 20 current or former Saints players participated in the bountyprogram, but that Vilma, Smith and Fujita were punished because they were defensive leaders who contributed large amounts to a pool that paid for big plays as well as injury-causing hits. The league said Hargrove was punished for obstructing the investigation when first interviewed by investigators in 2010.

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

Vilma and Ginsberg walked out of a June 16 appeal hearing early after Ginsberg raised his objections to the NFL’s handling of the entire investigation. The other three players, who were represented by NFLPA attorneys, sat through the hearing to observe the NFL’s presentation of evidence, but 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 has already punished the Saints harshly as an organization, concluding that general manager Mickey Loomis and head coach Sean Payton failed to put a stop to Williams’ bounty system despite warnings from the league at the end of the 2009 season.

The NFL suspended 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.

Williams, now with St. Louis, is suspended indefinitely.