WASHINGTON » The Air Force recorded an “appalling” number of reports of sexual assault last year even as it worked to curb misconduct in the wake of a sex scandal at its training headquarters in Texas, the service’s top officer told lawmakers today.

Gen. Mark Welsh, the Air Force chief of staff, said there were 796 reports of cases ranging from inappropriate touching to rape. The 2012 figure is a nearly 30 percent increase from 2011 when 614 cases were reported. The number could be much greater, Welsh said, because many cases are never reported at all.

“Calling these numbers unacceptable does not do the victims justice,” Welsh said. “The truth is, these numbers are appalling!”

Welsh’s testimony before the House Armed Services Committee underscores the challenges it and the other military branches face in stopping sexual assault within the ranks. Even more disturbing than the number of reports of sexual assault is the fact that most of these crimes are committed by fellow airmen, Welsh said.

The scandal at Lackland Air Force Base near San Antonio continues to unfold nearly two years after the first victim came forward. All U.S. airmen report to Lackland for basic training. The base has about 500 military training instructors for about 35,000 airmen who graduate every year. While one in five recruits are women, most instructors are men.

The preliminary results of Air Force investigation released in November described abuses of power by bad instructors who took advantage of a weak oversight system to prey on young recruits.

The investigation, which is ongoing, has found so far that 32 military training instructors allegedly engaged in inappropriate or coercive sexual relationships with 59 recruits and airmen at Lackland, according to the Air Force. Six instructors have been convicted in court martials on charges ranging from adultery, rape and conducting unprofessional relationships. Another nine instructors are awaiting courts martial. Two more received non-judicial punishments. There are 15 instructors still under investigation.

The Air Force has changed the way it selects officers and instructors who train new recruits and created a special unit of lawyers and investigators to assist victims of sexual assault.

Welsh said he has stressed to the Air Force’s officer corps and senior enlisted ranks the importance of eliminating sexual misconduct from the ranks. As part of that effort, Welsh issued a “Letter to Airmen” earlier this month that said images, songs and stories that are obscene or vulgar are not part of the Air Force heritage.

An Air Force veteran who pressed Congress to hold hearings on the misconduct at Lackland said there is a sexual assault epidemic in the military. Jennifer Norris said she medically retired in 2010 and was sexually assaulted while serving in the Air Force but not at Lackland. She told the committee she frequently has seen well-intentioned reforms fall short.

Fundamental reforms are needed “to change a military culture and fix the broken military justice system,” said Norris, who serves as an advocacy board member of the group Protect Our Defenders.