WASHINGTON — One after another, the charges have tumbled out — allegations of sexual assaults in the military that have triggered outrage, from local commanders to Capitol Hill and the Oval Office.

But for a Pentagon under fire, there seem to be few clear solutions beyond improved training and possible adjustments in how the military prosecutes such crimes. Changing the culture of a male-dominated, change-resistant military that for years has tolerated sexism and sexist behavior is proving to be a challenging task.

“Members of the Hill, people in the department and the American people have the right to be outraged,” Pentagon press secretary George Little said Wednesday, adding the military “must hold ourselves to a higher standard.”

As new sexual assault allegations emerged this week involving an Army soldier who was assigned to prevent such crimes — the second military member involved in similar accusations — the Pentagon said Defense Secretary Chuck Hagel is working on a written directive to spell out steps aimed at resolving the escalating problem.

But President Barack Obama, fuming at a news conference last week, warned that he wanted swift and sure action, not “just more speeches or awareness programs or training.”

The president has made very clear his expectations on this issue,” Little said, adding that Hagel told Obama on Tuesday about an Army sergeant first class at Fort Hood, Texas, who faces allegations of sexual misconduct. The case involves the soldier’s activities with three women, including an allegation that he may have arranged for one of them to have sex for money, according to a defense official.

Those allegations come on the heels of a Pentagon report last week that estimated that as many as 26,000 military members may have been sexually assaulted last year, based on survey results, out of 1.4 million in the services. That report, and a recent series of arrests and other sexual assault problems across the military, have triggered a rush of initiatives from the Pentagon and proposed legislation on Capitol Hill. But experts warn that stemming an increase in assaults will require concrete changes — both in law and in military culture.

“There is not a quick fix,” said Anu Bhagwati, former Marine captain and executive director of the Service Women’s Action Network. “The military can’t train its way out of this problem.”

Changing the culture in the military, to foster greater respect, she said may require using outside groups and advocates to deal with assault cases so that victims don’t feel intimidated by having to go to senior officers with their assault allegations.

According to Little, Hagel is considering changes to the Uniform Code of Military Justice that would prevent commanders from reversing sexual assault convictions, along with other efforts to improve training, assist victims and strengthen discipline. Hagel has ordered the retraining, recertifying and rescreening of all sexual assault prevention and response personnel, as well as military recruiters.

Sen. Kirsten Gillibrand, D-N.Y., plans to introduce legislation today that would reform the military justice system by taking top commanders out of the process of deciding whether a sexual misconduct case goes to trial. For sexual offenses with authorized sentences of more than one year in confinement that decision would rest instead with officers at ranks as low as colonel who are seasoned trial counsels with prosecutorial experience.

And, Sens. Claire McCaskill, D-Mo., and Amy Klobuchar, D-Minn., introduced legislation Wednesday to require the Pentagon to establish strict new criteria for service members who can serve in sexual assault prevention programs throughout the military.