In any given year, the hiring of new head coaches in the N.F.L. prompts hope and revival for millions of fans.

But when the most recent hiring cycle ended on Monday with the Houston Texans hiring Lovie Smith to fill the ninth and final open spot, the tally of minorities in such jobs was, to many civil rights leaders, disappointingly low.

Two of the nine vacancies, or 22 percent, were filled by minorities: Smith, who is Black, and Mike McDaniel of the Dolphins, who is biracial. That rate is consistent with past hiring cycles and brings the number of head coaches of color to five in the 32-team league. Smith and McDaniel join Ron Rivera of the Washington Commanders, Robert Saleh of the Jets and Mike Tomlin of the Pittsburgh Steelers.

But scrutiny of those numbers is far harsher this year after Brian Flores, an Afro-Latino coach who was fired by the Miami Dolphins last month, brought allegations of discrimination.

Last week, Flores sued the league and its teams in federal court, reigniting a complex and heated debate about race and equity in the country’s biggest league, and the efficacy of the N.F.L.’s primary tool for promoting diversity, the Rooney Rule.

The league has called the suit “without merit” but the number of nonwhite head coaches in the N.F.L. has continued to decline since the high-water mark of eight last set in 2017. There are just two more head coaches of color than when the Rooney Rule, which requires teams to interview people of color for vacancies in its top coaching and managerial ranks, was established two decades ago.

Since then, the league has tweaked and expanded the requirements to comply with the rule, but its attempts have yielded halting progress and fresh criticism that its efforts to diversify its senior ranks are insufficient. Yet there exists no consensus on how to move forward.

On Monday, several civil rights leaders met with N.F.L. Commissioner Roger Goodell and called for the Rooney Rule to be replaced.

“However well-intentioned, the effect of the Rooney Rule has been for team decision makers to regard interviews with candidates of color as an extraneous step, rather than an integral part of the hiring process,” said Marc Morial, the chief executive of the National Urban League. “The gravity of the situation is long past the crisis point.”

While Flores did not call for the Rooney Rule to be scrapped, he said that teams have been evading the intent of the rule by interviewing coaches of color, but never intending to hire them. He called these meetings “sham interviews” and took particular aim at the Giants and the Denver Broncos. Both teams said Flores was considered and interviewed as a legitimate candidate for their vacancies, which both went to white coaches.

On Monday, Flores’s lawyers issued a statement that congratulated Smith on his hire, but claimed that he had only been selected over Flores, who was a finalist for the job, because of Flores’s “decision to stand up against racial inequality across the N.F.L.”

Responding to the statement on Monday, Texans General Manager Nick Caserio said Flores’s lawsuit “didn’t really affect the process at all.”

Goodell signaled last week that the Rooney Rule would not be eliminated but needed to be strengthened, work he pledged to accomplish by having experts from outside the N.F.L. review their policies and by getting input from former coaches and players. In a letter to all club presidents and chief executives, he said that while the league had made strides in promoting diversity, “we must acknowledge that particularly with respect to head coaches the results have been unacceptable.”

Cyrus Mehri, a civil rights lawyer who was instrumental in creating the Rooney Rule in 2002, and who has continued to push for it to be strengthened, agreed that it should not be abandoned because progress had been slow.

“You build on the laws, you build on your infrastructure, you build on the tools, you don’t destroy them,” Mehri said. “I think that it’s misplaced to get rid of a rule that’s increased the selection rate for coaches by five or 10 times depending on what data you look at.”

But, Mehri acknowledged, the rule’s efficacy depends on implementation and enforcement, and those have been hard to consistently ensure.

The league has broadened the number of jobs that are covered by the Rooney Rule, adding senior positions like general manager and team president, and adding women to the interview requirement, with the most recent changes in 2021. A year earlier, the owners approved a proposal to change the league’s anti-tampering policy by prohibiting teams from blocking assistant coaches from interviewing for head coach or coordinator positions with other teams.

But the league’s owners declined to decide on a more contentious proposal that would have rewarded teams that hire women or people of color for head coach or general manager jobs with draft picks. Rooney Rule violations can prompt penalties that include fines assessed to team executives who lead hiring searches, but they are rarely imposed.

Unlike at publicly traded companies, where executives can be pressured by shareholders, employees and even the government, the N.F.L. is a collection of 32 independent franchises and rules must be adopted by their owners, who can be loathe to pass rules that limit their decision-making. Critics contend that unless the Rooney Rule is given more teeth, many teams will continue to do little more than what is required, which is why the number of head coaches remains stubbornly low.

“There is an accountability mechanism” at public corporations, said Nzinga Shaw, who worked in the human resources department at the N.F.L. and was a member of the league’s diversity council, and who now is the chief inclusion and diversity officer at ZRG, an executive talent agency. “Even though the N.F.L. is huge, because of the private nature of how it is governed, it is extremely hard to force the organization to do the right thing.”