The Air Force is investigating a growing sexual-misconduct scandal in its basic-training operations, with a dozen male boot-camp instructors under suspicion of assaulting, harassing or having sex with female recruits.

The case originated with a single complaint filed a year ago by a woman at Lackland Air Force Base in Texas. It has snowballed into potentially the worst sex scandal in the U.S. military since 1996, when 12 male soldiers were charged with abusing female recruits and trainees at the Army’s Aberdeen Proving Ground in Maryland.

The Air Force investigation centers on a unit of boot-camp instructors at Lackland, near San Antonio, where 36,000 recruits undergo basic training each year.

About one-quarter of the instructors in the 331st Training Squadron have either been charged with crimes or are under investigation for sexual misconduct. One trainer has been charged with raping or sexually assaulting 10 recruits.

Senior Air Force officials said they have found problems in other units as well, prompting them to open multiple investigations to determine the extent to which female recruits face harassment and whether the Air Force’s selection process for male instructors is fundamentally flawed.

“We are leaving no stone unturned,” Gen. Edward A. Rice Jr., the Air Force’s commander of training and education, said Thursday. “I am being as aggressive as I can.”

Rice was in Washington to brief lawmakers and senior Pentagon leaders on the status of the investigations. Last week, the Air Force relieved the commander of the 331st Training Squadron, Lt. Col. Michael Paquette, citing “an un­acceptable level of misconduct” by members of his unit.

The Air Force also appointed a two-star general to investigate whether the Lackland boot camp and other training centers suffered from “systemic issues” related to sexual misconduct.

Even as more women fill its ranks, the U.S. military has struggled to cope with the issue of sexual harassment and assaults. Despite numerous high-profile education campaigns and directives from the Pentagon, military officials acknowledge that a culture persists in which victims are re­luctant to report abuse.

Last year, about 3,200 incidents of sexual assault were reported or investigated by the armed services — a fraction of the estimated 19,000 cases that took place, according to Defense Department figures.

To address the problem, Defense Secretary Leon E. Panetta in April announced several policies designed to encourage victims to come forward and to require that all sexual-assault complaints be investigated by senior officers.

The Air Force has recently come under pressure from lawmakers to provide a fuller accounting of what happened at Lackland.

Rep. Jackie Speier (D-Calif.), a leading critic of the military’s record on sexual assault, has called on the House Armed Services Committee to hold hearings as it did in the Aberdeen scandal.

“This scandal is exploding at Lackland, and it is frighteningly similar to what happened at Aberdeen,” Speier said in a telephone interview.

Speier said the military needs to overhaul its judicial system so that sexual-assault cases are investigated and prosecuted outside the normal chain of command to remove the incentive for commanders to cover up incidents that could make them look bad.

At Lackland, the Air Force has filed charges against six instructors, with alleged wrongdoing ranging from rape to improper sexual relations with a trainee. Investigations into six other instructors are pending.

Air Force officials said that most of the misconduct occurred during basic training but that in some cases, instructors engaged in improper sexual relations with recruits after they had moved on to other training programs.

All told, the Air Force has identified 31 victims, each of whom remains in the service.

Rice, the Air Force general in charge of training, said the problems at Lackland surfaced in June 2011 when a female recruit reported being sexually harassed. Four months later, he said, three instructors in the 331st Training Squadron reported that misconduct among their fellow trainers was more widespread.

Advocacy groups said one of the biggest obstacles to preventing sexual abuse in the military is a culture of silence.

“For every instructor that assaults a recruit, there are usually dozens of others who have known about the problem,” said Anu Bhagwati, a former Marine officer and executive director of the Service Women’s Action Network.

About 22 percent of the Air Force’s recruits are women, but only about 11 percent of its training instructors are female.

Bhagwati called boot camp “a target-rich environment” for sexual abuse because instructors wield total authority over raw recruits.

“It’s the kind of environment where you’re being yelled at 24-7, where you’re terrified of everybody around you,” she said. “How are you supposed to ask for help if you’re the victim of sexual assault?”