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 years-long 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. “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 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 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 spokesman, Rose Richeson, declined to make the results of the April 28 meeting public, saying it would be “too premature to provide an interview.”