Reports of military sexual assaults jumped by 13% last year, but an anonymous survey of service members released on Thursday suggests the problem is vastly larger.

The survey results found that more than 20,000 service members said they had experienced some type of sexual assault, but only a third of those filed a formal report.

The survey number is about 37% higher than two years ago, when one was last done, fueling frustration within the defense department and outrage on Capitol Hill.

“I am tired of the statement I get over and over from the chain of command: ‘We got this, madam, we got this.’ You don’t have it!” Senator Kirsten Gillibrand, a New York Democrat, shouted during a Senate armed services committee confirmation hearing on Thursday for the army general James McConville. “You’re failing us.”

McConville has been nominated to be the next chief of staff of the army, and that service saw a surge of more than 18% in the number of sexual assault reports filed last year. The US Marine Corps had the largest jump, at 23%, while the navy saw a 7% increase and the air force figure was up by about 4%.

The Pentagon releases a report every year on the number of sexual assaults reported by troops. But because sexual assault is a highly underreported crime, the department sends out an anonymous survey every two years to get a clearer picture of the problem.

The increase in assaults has triggered another round of Pentagon programs to try to reduce misconduct.

Nate Galbreath, deputy director of the Pentagon’s Sexual Assault Prevention and Response Office, told reporters on Thursday that the latest numbers were “disheartening and it personally makes me angry”, but he said he was “not without hope”.

The sharp increase in reported marine assaults comes on the heels of two troubled years for the Corps. In 2017, the service was rocked by a huge online nude-photo sharing scandal, and later it launched a large public campaign to raise awareness of inappropriate behavior and increase enforcement. Nearly 60 service members eventually faced some type of punishment.

Gen Robert Neller, commandant of the US marines, said on Thursday that his troops “cannot truly be loyal to our nation without first being loyal to each other. All marines must be involved in preventing and addressing sexual assault and harassment.”

Col Kathy Turner, an army spokeswoman, said leaders must enforce standards to ensure a healthy command climate and prevent sexual misconduct by soldiers.

The survey found that young and junior enlisted women between ages 17 and 20 were most likely to experience sexual assault. In the vast majority of the cases the alleged perpetrator was a military man, often near the same rank as the victim and usually someone she knew. The report also found that nearly two-thirds of all incidents involved alcohol use by the victim and/or the offender.

Galbreath said the department had to reassess why prevention programs were not working as well with younger troops and adjust those efforts to better reach them. Programs that worked a few years ago, he said, were no longer effective.

The studies also found that there were often more problems in military units that had poor command climates or low levels of unit cohesion.

Last year, when the Pentagon announced that assaults in 2017 had increased by 10% over 2016, the then defense secretary, Jim Mattis, called the problem a cancer in the ranks and ordered the department to redouble its efforts to prevent and respond to sexual assaults. On Thursday, the acting defense secretary, Patrick Shanahan, called this year’s increase unacceptable and directed the military to enact new programs to identify serial offenders and increase scrutiny of new recruits to ensure they have the right character for military service.

“Sexual assault and sexual harassment are persistent challenges,” Shanahan said in a memo to military service leaders. “We cannot shrink from facing the challenge head on. We must, and will, do better.”

Galbreath said one change expected to begin later this summer will have the military begin comparing information on offenders from victims who file so-called “restricted” reports. Filing a restricted report allows victims to seek treatment but they avoid any criminal complaint or prosecution. Many victims choose that route to skirt any potential retribution or stigma of a public trial.

Under the new plan, Galbreath said the military would put information on alleged attackers into a database so repeat offenders can be identified. Galbreath said if officials found a possible repeat offender, they would go back to the victims to see if they might change their minds and agree to prosecute.

According to the survey, 21% of the women who said they reported a sexual assault also said that they suffered some type of retaliation aimed at stopping them from making a complaint.