He and Dempsey spoke one day after all of the military's leadership were summoned to the White House to discuss the sexual assault problem with President Barack Obama, who has expressed impatience with the Pentagon's failure to solve it.
At his Pentagon news conference, Hagel said it has become clear to him since taking office in February that holding people accountable for their actions is important, but simply firing people is not a solution. He said he gets a lot of advice on that.
He said some ask him, "Well, why don't you just fire some people?" He said his answer is, "Well, yeah, we could do that. And, you know, who are you going to fire?"
Hagel signed a one-page memorandum addressed to the uniformed chiefs and civilian heads of each of the military services requiring that the credentials and qualifications of all recruiters, sexual assault response coordinators and sexual assault victim advocates be reviewed to ensure that they meet current standards. They also will be given refresher training on professional ethics and the impact of violations.
"I am concerned that this department may be nearing a stage where the frequency of this crime and the perception that there is tolerance of it could very well undermine our ability to effectively carry out the mission, and to recruit and retain good people," Hagel wrote.
A catalyst for congressional outrage has been the disclosure in recent days of at least two cases in which a military member with responsibility for sexual assault prevention programs has himself been accused of sexual misconduct. Cases of sexual assault allegations against military recruiters also have arisen recently.
Dempsey, who has been among the most outspoken Pentagon official on this topic, called sexual assault in the military "a crime that demands accountability and consequences."
"As the president made clear to us yesterday, we can and must do more to change a culture that has become too complacent," Dempsey said. "We have a serious problem that we must solve: aggressive sexual behavior that rips at the bond of trust that binds us together."
Earlier Friday, the Air Force's top general said that sexual assaults in his branch of the military typically involve alcohol use and can be traced to a lack of respect for women.
"We have a problem with respect for women that leads to many of the situations that result in sexual assault in our Air Force," Gen. Mark Welsh told reporters in a lengthy interview in his Pentagon offices.
Welsh said combatting the problem, which he characterized as a crisis, is his No. 1 priority as the Air Force chief of staff. He said he reviews every reported case of sexual assault; last year there were 792 in the Air Force.
Welsh addressed criticism about his comment last week, in response to questions at a congressional hearing, that the problem can be explained in part by a "hook-up mentality" in the wider society. Some said his remark implied that the blame rests mainly with victims.
"If I had this to do over again, I would take more time to answer the question and not try to compress it," he said, adding that his point was that every person who enters the Air Force needs to be instructed in "this idea of respect, inclusion, diversity and value of every individual."
"Now, I didn't say it that way in the hearing, and I wish I had because I think it gave, especially victims, the opportunity for someone to interpret what I said as blaming the victims," he said, adding that as a result, "I am sorry about that because there is nothing that is farther from the truth."
Obama said after Thursday's meeting with the military leaders that he is determined to eliminate the "scourge" of sexual assault in the military, while cautioning that it will take a long and sustained effort by all military members.
"There is no silver bullet to solving this problem," Obama said.
"We will not stop until we've seen this scourge, from what is the greatest military in the world, eliminated," he told reporters.
Senior military officers are speaking about the problem with increasing bluntness and expressions of regret. Dempsey, the Joint Chiefs chairman, on Wednesday called it a "crisis" in the ranks, and on Thursday the Army chief of staff, Gen. Ray Odierno, publicly acknowledged his service's efforts are "failing."
"They care about this and they are angry about it," Obama said.
"Not only is it a crime, not only is it shameful and disgraceful, but it also is going to make and has made the military less effective than it can be," the president said.
Those summoned to the White House by Obama included not just Hagel, Dempsey and the chiefs of each military service but also the civilian heads of each service and senior enlisted advisers.
"I heard directly from all of them that they are ashamed by some of what's happened," Obama said.
The president added that because assault victims may be more likely now to come forward with complaints, the number of reported assaults may increase in the short run.
"I then want those trend lines to start going down because that indicates that we're also starting to fix the problem and we've highlighted it, and people who are engaged in despicable behavior, they get fully punished for it," Obama said.
The problem, which has plagued the military for decades, has been thrust to the fore by recent cases, including that of an Air Force officer who headed a sexual assault prevention office but was himself arrested for sexual battery.
On Thursday, Army officials said the manager of the sexual assault response program at Fort Campbell, Ky., had been relieved of his post after his arrest in a domestic dispute with his ex-wife. The program he managed was meant to prevent sexual harassment and assault and encourage equal opportunity.
"It is time we take on the fight against sexual assault and sexual harassment as our primary mission," Odierno said.
A Pentagon report last week 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.