For nearly a decade, the president of the Washington Football Team sent emails to a friend in which he casually joked about Native Americans and racial and political diversity, griped about referees and league initiatives to improve player safety, and arranged tickets and perks for his correspondent. He also thanked the man for getting a fine lifted and for understanding the team’s thorniest troubles.

That man was Jeff Pash, who — as the longtime general counsel of the N.F.L. and a top adviser to Commissioner Roger Goodell — would become responsible for investigating the team that had been run by the very executive he grew close to.

Pash appeared to engage willingly in the back-and-forth, sometimes reassuring the Washington executive, Bruce Allen, who was with the club from 2009 to 2019, not to worry about troubles that would eventually rock the team and the league, including reports about harassment of the club’s cheerleaders.

A trove of 650,000 emails gathered in the league’s investigation of workplace misconduct in the Washington Football Team’s front office has already resulted in the resignation of Jon Gruden as coach of the Las Vegas Raiders, after The New York Times published messages in which he made racist, sexist and homophobic remarks. The league received access to the emails several months before the investigation was completed last summer.

But Allen’s exchanges with Pash, sent from 2009 to 2018, reveal a larger story about a clubby relationship between a top league official and team executives and owners he is expected to oversee.

When the N.F.L. fined the Washington Football Team $15,000 for manipulating its player injury report, Allen reached out to Pash and the penalty was rescinded. In another email, Allen expressed concern that the commissioner would accuse him of breaking rules on the signing of free agents, prompting his friend to reassure him, “He knows who it is and that it is not you.”

And after a crisis erupted over allegations of sexual harassment of the Washington cheerleaders, Allen contacted Pash, who offered reassuring words.

“I know that you are on it and would not condone something untoward,” he told Allen.

In emails not involving Pash, however, Allen, Gruden and other men had shared photos of women wearing only bikini bottoms, including one picture of two Washington team cheerleaders.

Pash joined the league in 1997, intersecting with Allen, who was a longtime Raiders and Buccaneers executive before he landed in Washington. Their emails suggest that, when the Washington franchise was in crisis, Pash tended to offer a sympathetic shoulder rather than acting as an impartial arbiter.

“Communication between league office employees and club executives occurs on a daily basis,” Jeff Miller, the league’s executive vice president of communications, said in a statement Thursday. “Jeff Pash is a respected and high-character N.F.L. executive. Any effort to portray these emails as inappropriate is either misleading or patently false.”

After The New York Times contacted the league, the owners of the Arizona Cardinals, Chicago Bears and the Giants expressed support for Pash.

Neither Pash nor Allen responded to a request for comment.

In May 2018, the Washington Football Team faced a scandal over the sexist treatment of its cheerleaders, who The Times revealed had been flown to Costa Rica for a team event, made to pose topless for a photo shoot and assigned as personal escorts to team sponsors and suite holders.

After a second Times article, about cheerleaders who were hired mainly for their appearance and did not cheer, the team conducted an internal investigation and promised to focus on cheerleader safety. In December 2019, after the team struggled all season, Allen was fired.

Eight months later — amid a dispute between the team’s principal owner, Daniel Snyder, and his limited partners and as The Washington Post detailed widespread sexual harassment in the organization — Snyder hired the Washington lawyer Beth Wilkinson to conduct an investigation. The league took over the investigation, with Wilkinson reporting to Pash.

Ultimately, Snyder expanded his financial stake in the team, and the league did not release the full detailed report of its investigation.

This July, the team was fined a record $10 million; Snyder agreed to stay away from the team’s offices for several months; and consultants were hired to monitor the team’s human resources practices.

In October 2013, an N.F.L. executive had turned down Allen’s appeal of a $15,000 fine because the team’s coach at the time, Mike Shanahan, had doctored the injury report. Allen wrote back to Pash and the other league officials copied on the email: “BS.”

Pash overruled his staff’s decision to issue the fine, replying to Allen’s email by saying that the team did not need to pay the $15,000 “or any other amount with respect to this matter and you should consider the fine to be rescinded in its entirety.”

The two also seemed to commiserate on politics and some of the league’s struggles with diversity and inclusion, including its hiring practices.

Pash sympathized with Allen’s frustration over the 2016 hiring of Jocelyn Moore, a Black woman who became the league’s chief lobbyist on Capitol Hill after working for several Democratic senators.

“Curious — is there a rule against hiring Libertarians, Independents or even a Republican?” Allen asked.

“No,” Pash replied, “but it can sometimes look that way!”

Referring to a rule that requires N.F.L. teams to interview minority candidates for coaching and executive jobs, Allen said, “We have the Rooney rule …. So I’m going to propose a Lincoln Rule at the next meeting.”

Pash and Allen, as his team spun in and out of crises, joked about the league’s diversity initiatives.

When Allen shared an audio file of a team song aimed at attracting Latino fans, Pash responded, “I am not sure this song will be as popular after the wall gets built.”

Pash helped Allen defend the team’s former name, widely viewed as a slur of Native Americans, against criticism. In May 2014, Allen sent Pash an article that said that Senator Maria Cantwell of Washington — a vocal critic of the team’s name — went to a high school that still had a mascot with Native American imagery for its sports teams.

Pash responded: “No way. Too good to be true.”

Pash and Allen shared their love of former President Dwight D. Eisenhower and lamented the course of the country during the Obama administration. With mock formality, Pash referred to Allen as “Mr. President,” while Allen addressed Pash as “Counselor.” They flattered each other and sent notes of praise after presentations at league meetings, appearances on television and victories on the field and in the courtroom.

They joked about Hooters, the restaurant chain known for the skimpy outfits of its wait staff, and about Allen’s pull with the company, which was co-founded by his friend Edward C. Droste.

“PS — The Hooters at Fedex Field has been reserved for the post game celebration,” Allen wrote to Pash in 2011 after the general counsel and his legal team fought the players union in court during a lockout of its members.

A year later, when the league penalized Washington and Dallas for violating league spending limits, Allen asked to speak with Pash. “Still talking internally about this,” Pash replied. “I am not making any promises as to an outcome. But I can assure you that I am not blowing you off.”

After Allen thanked him, Pash added: “We may not see this the same way. But that does not change my respect or affection for you. After all, nobody else has ever given me a Hooters VIP card.”

Sprinkled into the correspondence about league business are notes highlighting Allen and Pash’s close friendship. When Allen’s brother, George, ran for U.S. Senate in Virginia in 2012, Pash donated $1,000 to his campaign. Pash was not shy about saying how much his wife and family loved the team, and Allen sent Pash the club’s fight song after rare Washington victories.

At Christmas and New Year’s, the pair exchanged heartfelt holiday greetings, with Pash emailing in January 2013 to congratulate Allen on making the playoffs. “Happy New Year — even though 2012 was not the easiest year in many respects, I continue to value our relationship and your advice,” Pash wrote.

Allen and Pash, who routinely referred to their apparently weekly phone calls as “rants,” were united in their disdain for the head of the N.F.L. Players Association, DeMaurice Smith, Pash’s adversary in the 2011 labor negotiations.

In September 2010, Allen told Pash that his decision not to give Smith a field pass to a Washington home game had angered Smith. “New sheriff in town,” Pash responded to Allen, who was in his first year with the club.

Allen told Pash that a union spokesman would call Snyder to complain. “That should be a short conversation,” Pash replied.

A few years later, Pash wrote to Allen asking to speak. “Please give me a few minutes — I’m trying to lower a player’s salary at the moment,” Allen responded. Pash wrote back, “The Lord’s work.”

Early on the morning of March 11, 2011, the first day of a work stoppage by players, Pash and Allen’s email thread discussing the dispute ended in a way that typified their relationship.

After Pash thanked Allen for sending him team gear and called Allen “a special guy,” Pash gushed about their bond: “Even when our employers were, shall we say, at odds, you treated me with kindness and courtesy. I have never forgotten that. Over the years you have been a frequent source of excellent advice.”