NFL Commissioner Roger Goodell (Nam Y. Huh/The Associated Press)

NFL Commissioner Roger Goodell said Monday he has informed Redskins officials that the league will not consider lessening the two-year, $36 million salary cap penalty imposed on the team last year.

“I’ve told the Redskins directly that there will be no change in that modification to their cap,” Goodell said at a news conference during a midday break in the NFL’s annual meeting at  a Phoenix resort.

Goodell said he and other NFL officials met with Redskins representatives twice within the past month to discuss the matter.

“I did meet with the Redskins — so did our staff — on, I think, two occasions over the last 30 days to make sure we fully understood their position [and] they understood our position,” Goodell said. “But as I said earlier, there will be no change.”

The Redskins declined to comment through a spokesman.

Goodell declined to say whether the league prepared for the possibility that the Redskins might take legal action in the case, saying: “They have to speak to that.”

He also did not respond to last week’s characterization by Redskins General Manager Bruce Allen that the salary cap reduction is “a travesty of fairness.”

Said Goodell: “I don’t have a reaction to it.” The Redskins must absorb the remaining $18 million of the two-year, $36 million penalty this season.

People familiar with the case said Sunday the league had informed the Redskins that it would not yield on the salary cap reduction, in part because it saw no reason to do so and in part because any modification to the penalty would have to be ratified by both the other owners and the players’ union. Those groups approved the original salary cap penalties given to the Redskins and Dallas Cowboys, whose cap space was reduced by $10 million over two years.

Those people with knowledge of the case said that message had been delivered personally by Goodell–as Goodell confirmed Monday–and by other league officials.

Allen and Redskins Coach Mike Shanahan said last week they remained hopeful of  recouping some of the team’s lost salary cap space in the future. They did not specify how they hoped to accomplish that.

Allen denied last week that the Redskins had contemplated legal action in the matter. But he said the team would “always look at our options.”

Several people who were in contact with the Redskins in recent weeks said they’d been told by team officials that litigation was a possibility.

The league, with the consent of the players union, imposed the cap reductions on the Redskins and Cowboys last year, ruling that the teams attempted to gain an improper competitive advantage by the way they structured players’ contracts during the 2010 season, when the NFL had no salary cap. The teams challenged the salary cap penalties via arbitration last year but their case was dismissed.

The Redskins, in large part because of the penalty, have made several moves to get beneath the $123 million salary cap and proceeded cautiously in free agency.