PALM BEACH, Fla. — The N.F.L. team owners are grappling with several weighty issues at the league’s annual meeting this week that clash with the setting at the posh Breakers Hotel.

Topping the list is the lawsuit brought by the former Miami Dolphins head coach Brian Flores, who in February accused the league and its 32 teams of discriminating against him and other Black coaches in their hiring practices.

A pretrial conference for the federal lawsuit, in which Flores detailed what he called “sham” interview processes with the Giants this year and the Denver Broncos in 2019, is scheduled for April 29. Flores expects to file an amended complaint, according to court filings, and can do so until April 8. The N.F.L. will have 45 days to respond once Flores files.

Several team owners and coaches at the meetings, which host all top league personnel each year, suggested that the league will push back forcefully against Flores’s claims, which were largely precipitated by a text from New England Patriots Coach Bill Belichick, who inadvertently messaged Flores that the Giants were going to hire Brian Daboll, the offensive coordinator of the Buffalo Bills, three days before Flores’s interview with the team.

John Mara, the co-owner of the Giants, said on Sunday that no one in his organization was in contact with Belichick.

“The allegations are false,” Mara said. “We’re very comfortable with our hiring process. It was a fair process and we ended up making the decision that we made based on a lot of factors, none of which had to do with race.”

Mara said he would say the same comments under oath if he was deposed in the case, adding that he was “not settling” the lawsuit.

Belichick, also speaking with reporters for the first time since the lawsuit was filed, declined to answer questions about his text messages to Flores.

Flores also alleged in his lawsuit that Stephen M. Ross, the Dolphins’ owner, pressured him to tank the 2019 season and offered him $100,000 for each game the team lost. As of Monday afternoon, Ross had not yet spoken with reporters during the meeting.

The N.F.L. is expected to argue that the Flores case is an internal league matter and should be heard by an arbitrator, not a federal judge.

The Flores case once again laid bare the fact that the N.F.L., after decades of efforts to increase the diversity of its coaching and executive ranks, has just three Black head coaches — the Pittsburgh Steelers’ Mike Tomlin, the Houston Texans’ Lovie Smith and the Dolphins’ Mike McDaniel, who identifies as biracial — in a league predominantly populated by Black players.

Flores was fired by the Dolphins in January and, after failing to land another head coaching job this off-season, was hired by Tomlin and the Steelers as a senior defensive assistant/linebackers coach. Tomlin said he was in “continual conversation” with Flores after the lawsuit was filed.

“I wanted to support him as a member of the football coaching fraternity, and really just informal discussions,” Tomlin said, adding that the conversation about hiring Flores in Pittsburgh resulted from those talks. “And it really moved rather quickly to be quite honest with you. We didn’t breach the subject until all the head jobs were filled.”

On Monday morning, Tomlin said he was not confident that the league’s next steps would lead to better outcomes. Later in the day, the league announced that it would keep the Rooney Rule, which was implemented in 2003 to compel teams to interview nonwhite candidates for head coaching and executive positions. Commissioner Roger Goodell had said before the Super Bowl that the league would consider overhauling the rule. According to the N.F.L. minority coaching hires increased to 39 percent, up from 35 percent, across all coaching positions in the 2021 cycle. The league also decided to include women in Rooney Rule requirements for head coach and general manager openings. The rule will now stipulate that each team must conduct in-person interviews with two external candidates who are people of color and/or women, thought it has the potential to create a loophole that could actually decrease the number of candidates of color interviewing for top jobs.

The N.F.L. also announced the creation of a six-person diversity advisory committee. Its members include Rick Smith, the former Houston Texans general manager, and Peter Harvey, the former New Jersey attorney general who advised the league on its 2017 investigation into domestic violence allegations against Dallas Cowboys running back Ezekiel Elliott.

Lovie Smith, who spent 11 years as a head coach of the Chicago Bears and the Tampa Bay Buccaneers before being hired to lead the Texans, said the only thing he can do is hire more coaches of color and hope that other teams and their owners do the same.

“We all have to look at what we can do,” Smith said. “We can put more guys who look like us in positions to show exactly who they are. Then the owners can decide who they want leading their franchises. That’s the only question those 32 guys can answer.”