Jon Gruden, the head coach of the Las Vegas Raiders, in 2011 used racist terms to denounce DeMaurice Smith, the executive director of the N.F.L. Players Association, who is Black and is now facing opposition within the union to the extension of his contract.

The email surfaced just hours before the player representatives for the 32 teams were expected to vote on whether to give Smith a fifth term as the union’s leader without having to hold a general election. Smith was not endorsed by the union’s selection committee earlier this week, a sign that he faces unusually stiff opposition within his own ranks. Some players have accused Smith of being too conciliatory to the league.

There is reason to believe the league’s owners would prefer that he stay, and such an inflammatory email, first reported by The Wall Street Journal and confirmed by The New York Times, complicates the vote for players who oppose Smith.

While Smith has been combative with the N.F.L. at times, he is viewed favorably by many owners who worked closely with him last season to get the players back on the field during the pandemic.

The email was written in 2011 in an exchange between Gruden, who is white and was an analyst for ESPN at the time, and Bruce Allen, who was then the president of the Washington Football Team.

“Dumboriss Smith has lips the size of michellin tires,” Gruden wrote about Smith, who is Black, in the exchange.

The email was discovered during a review of workplace misconduct at the Washington Football Team that ended this summer. During the past few months, the N.F.L. commissioner, Roger Goodell, told league executives to look at more than 650,000 emails, including the one that included Gruden’s comment. This week, the executives presented a summary of that review to Goodell and shared with him the Raiders emails pertaining to Gruden.

“The email from Jon Gruden denigrating DeMaurice Smith is appalling, abhorrent and wholly contrary to the N.F.L.’s values,” Brian McCarthy, a league spokesman, said in a statement.

The league declined to say whether Gruden could face disciplinary action.

Smith said in a statement that Gruden's comments are symptomatic of the challenges that Black Americans face.

“You know people are sometimes saying things behind your back that are racist just like you see people talk and write about you using thinly coded and racist language,” said Smith, who took over as the union’s executive director in 2009. “Racism like this comes from the fact that I’m at the same table as they are and they don’t think someone who looks like me belongs.”

Mark Davis, the Raiders’ owner, called Gruden’s email “disturbing and not what the Raiders stand for.” He added that the team first learned about the email on Thursday and is reviewing “it along with other materials provided to us today by the N.F.L.”

“We are addressing the matter with Coach Gruden and will have no further comment at this time,” Davis said.

Gruden said that he did not recall the email, but acknowledged that in 2011, he was angered by the stalled labor talks between the league and union which led the owners to lockout the players.

“I probably looked at De as the villain,” he told The Athletic on Friday. “And I was really upset that there was going to be a lockout.”

He added that “I went too far calling him the Michelin lips. I never had a blade of racism in me” and that he “used a terrible way to insult a guy.”

Gruden said he called Smith but had not heard back.

Gruden was working in 2011 as an analyst for “Monday Night Football,” three years after leaving a head coaching job at the Tampa Bay Buccaneers. In 2018, he signed a 10-year contract to coach the Raiders, when the team was still playing in Oakland, Calif.