WASHINGTON — The Air Force’s top general appeared to be losing his cool. But it wasn’t over a controversial plan to scrap an aircraft prized for protecting ground troops or billions of dollars in cuts that are straining a service striving to recover from the grind of 12 years of war.

“The single biggest frustration I’ve had in this job is the perception that somehow there is religious persecution inside the United States Air Force,” Gen. Mark Welsh III told a House Armed Services Committee hearing earlier this spring. “It’s not true.”

Welsh’s irritation underscored the pressure the Air Force is under from Republicans in Congress, evangelical Christians and conservative advocacy groups to end what they allege is the service’s suppression of religious freedom. Their charge isn’t new, but the target is: a regulation designed to prevent religious bias by barring commanders and other leaders from “the actual or apparent use of their positions to promote their religious convictions to their subordinates.”

The controversy represents the latest chapter in the Air Force’s yearslong struggle to balance the constitutional right of freedom of faith with the Constitution’s prohibition on the governmental promotion of religion.

“It’s when the commander becomes the preacher that we have a problem,” said a former senior defense official who dealt with the issue but requested anonymity in order to speak freely. “It’s commanders turning to subordinates and saying, ‘Here’s what makes my life worthwhile. It’s going to my church and subscribing to my views.’ ”

Opponents counter that the regulation is constitutionally questionable and contravenes provisions Congress inserted into the Pentagon’s last two budgets requiring the military to “accommodate individual expressions of belief” unless “it could have an adverse impact on military readiness, unit cohesion and good order and discipline.”

“The Air Force religious freedom regulations and practices are inconsistent with the Constitution and with current law,” 20 House of Representatives Republicans wrote in an April 15 letter to Air Force Secretary Deborah Lee James. The regulation “introduces a subjective and unworkable restriction on a leader’s ability to speak about their faith.”

The Air Force defends the regulation as a measure that “seems to make good sense.” Yet the pressure — legislation, congressional hearings, meetings, letters, media statements and online appeals — to revise or dump it is having an impact.

Late last month, James and Welsh convened a “Religious Freedom Focus Day” conference of senior chaplains and legal and manpower officials to discuss the policy. An Air Force spokeswoman, Rose Richeson, declined to make the results of the April 28 meeting public, saying it would be “too premature to provide an interview.”

But Tony Perkins, the president of the Family Research Council, a Christian conservative policy institute that leads a coalition of organizations that are fighting the regulation, said that based on what he’d heard from people at the meeting he expected the Air Force to “make a policy change shortly.”

The prospect alarms supporters of the policy, who say a pro-Christian bias in the Air Force remains overwhelming and that the regulation provides an avenue of relief to service members who object to being regaled with their superiors’ religious views or who worry that declining invitations to “voluntary” Bible classes might jeopardize their fitness reports and chances of promotion.

The regulation has been “an umbrella in a tsunami of Christian fundamentalist extremism,” asserted Mikey Weinstein, the head of the Military Religious Freedom Foundation and a former Air Force officer whose outspokenness has won him scorn and death threats.

Since the regulation went into effect, 4,121 Air Force personnel have sought the organization’s help in fending off proselytizing by superiors, Weinstein said. The organization has a 95 percent “success rate” in ending “the offending behavior,” he said. Evangelical Christians draw the largest number of complaints — ironically enough, from fellow Christians, he said.

There’s little disagreement about the importance that the free practice of religion plays in ensuring the cohesion, morale, “good order and discipline” of military units. But the regulation says superiors who proselytize “may cause members to doubt their impartiality and objectivity.”

“The potential result is a degradation of the unit’s morale, good order and discipline,” the regulation says. “Airmen, especially commanders and supervisors, must ensure that in exercising their right of religious freedom, they do not degrade morale, good order and discipline in the Air Force or degrade the trust and confidence that the public has in the Air Force.”

The regulation grew out of a 2005 uproar over proselytizing by evangelical Christians and Weinstein’s allegations of religious discrimination at the U.S. Air Force Academy, at Colorado Springs, Colo.

Since then, the Air Force has worked hard “at balancing … free expression of religion with the needs of the military and not giving the appearance or an actuality of forcing anything or appearing to force,” James told the Senate committee.

Not so, said Perkins of the Family Research Council, which issued a report in March that included a long list of alleged incidents ranging from officers ordered to remove Bibles from their desks to retaliation against personnel for expressing opposition to same-sex marriage.

“The Air Force for some reason has done the worst in terms of violating the religious freedom of its personnel,” Perkins charged. The result has been a “chilling effect” on leaders’ rights to religious expression, he said.

“We don’t advocate that someone in a position of authority use that authority to somehow force someone to participate in a religious activity,” Perkins said. “On the flip side of that is just because someone in a command position (has) a devotional or weekly Bible study and you invite your colleagues, there is nothing wrong with that as long as you are not requiring (attendance). It’s like asking someone to come play dominoes.”

Military culture, however, is very different from the civilian world, the regulation’s defenders responded. The services are closed, clannish and hierarchical, and in such an atmosphere a commander’s exhortation to follow his or her beliefs or an invitation to a voluntary prayer circle can be perceived as tantamount to an order.

To illustrate the point, Weinstein said his organization had received 17 complaints — all from Protestants — in early May after a commander at an Air Force base left invitations to a “Purity Ball” — a religious, high school promlike event attended by fathers and daughters — on the chairs of three senior subordinates. The girls take vows to refrain from premarital sex.

The subordinates “understood that they had to distribute the invitations. They distributed them to 212 people,” said Weinstein, who declined to identify the base, the commander or the complainants because of confidentiality considerations.

When one of the complainants confronted the commander with the no-proselytizing regulation, the commander refused to rescind the invitations but agreed not to distribute them next year, Weinstein said.

The commander, he added, declined to issue a statement acknowledging that his action violated the regulation because his superior would see it.