RAY SUAREZ:The problem of sexual assaults in the nation's armed forces is getting worse, and maybe much worse. The issue drew the national spotlight today and a presidential rebuke.

PRESIDENT BARACK OBAMA:We're not going to tolerate this stuff, and there will be accountability.

RAY SUAREZ:The news of growing sexual assaults in the military raised the president's hackles at a news conference with the president of South Korea.

PRESIDENT OBAMA:Let's start with the principle that sexual assault is an outrage. It is a crime. That's true for society at large, and if it's happening inside our military, then whoever carries it out is betraying the uniform that they're wearing.

RAY SUAREZ:Mr. Obama spoke as an annual Pentagon study reported sexual assaults in the military rose from just under 3,300 in 2012 to nearly 3,400 last year. But it also found that up to 26,000 cases went unreported.

At a Senate hearing this morning, the Air Force chief of staff, Gen. Mark Welsh, struck sparks with New York Sen. Kirsten Gillibrand, suggesting it's not always a commander's fault if victims don't come forward.

GEN. MARK WELSH, U.S. Air Force: The things that cause people to not report are—primarily are really not chain of command. It's: I don't want my family to know. I don't want my spouse to know or my boyfriend or girlfriend to know. I'm embarrassed that I'm in this situation.

It's the self-blame that comes with the crime. That is overridingly on surveys over the years the reasons that most victims don't report. And I don't think it's any different in the military. Prosecution rates in the Air Force for this crime ...

SEN. KIRSTEN GILLIBRAND, D-N.Y.: I think it's very different in the military. I think you're precisely wrong about that. Everything is about the chain of command.

RAY SUAREZ:The president said today the military has to exponentially increase its efforts to address the problem. And Defense Secretary Chuck Hagel announced he's issuing new orders to change the culture in the ranks.

DEFENSE SECRETARY CHUCK HAGEL, United States: Together, everyone in this department at every level of command will continue to work together everyday to establish an environment of dignity and respect, where sexual assault is not tolerated, condoned or ignored.

RAY SUAREZ:The Pentagon report came just days Lt. Col. Jeffrey Krusinski, who runs the Air Force unit on sexual assault, was himself arrested for allegedly groping a woman. And, in February, Air Force Lt. Gen. Susan Helms overturned a captain's conviction on aggravated sexual assault.

Now Missouri Sen. Claire McCaskill is holding up Helms' nomination for vice chair of the U.S. Space Command. She spoke at today's hearing.

SEN. CLAIRE MCCASKILL, D-Mo.: The general said, no, no, we believe the member of the military. That is the crux of the problem here, because if a victim does not believe that the system is capable of believing her, there's no point in risking your entire career.

RAY SUAREZ:In response, lawmakers are pursuing multiple kinds of legislation on the problem. One could strip commanding officers of their ability to reverse convictions.

I'm joined now by Mark Thompson, the Washington deputy bureau chief and national security correspondent for TIME and writer of the Battleland blog.

And, Mark, you have seen the reports. You have seen the Pentagon's self-reporting on this. Does that 26,000 unreported assaults a year look like a solid number? Where does it come from?

MARK THOMPSON, TIME: Well, it's an extrapolated number, Ray, from anonymous phone surveys done by the Pentagon of military people. And so it's sort of squishy to begin with.

What's particularly striking about the number, of course, is from 2010 to 2012, that number grew by 35 percent, whereas the hard number, the number of cases that actually were brought forward by people complaining about sexual assaults in the military only went up by roughly six percent from 3,200 to 3,400.

So even though they are getting more reports, those that are unreported are going up even faster.

RAY SUAREZ:Well, a number of unreported cases nine times larger than the number of reported cases ...

MARK THOMPSON:Right.

RAY SUAREZ:... is that bigger than the service chiefs even realized at first?

MARK THOMPSON:Well, I think, number one, it is bigger than what you see in the civilian world, where the proportion of reported is an order or two bigger than what you see in the military.

But this is not a new problem. This is a longstanding problem. I was on this show 16 years ago talking about it. It remains a problem, what's happening. You have got about 14 percent of the military in uniform that are women, and all of a sudden, with these female senators, several of which we just saw, this is not being able to be ignored by the chiefs, the secretary of defense or anybody else.

It seems like we may have reached a turning point this weekend with the arrest of this Air Force officer.

RAY SUAREZ:Today, at the news conference at the Pentagon, the general in charge of overseeing the management of this problem flipped this on its head in a way and said that part of it is that there's more reporting.

MARK THOMPSON:Yes, I think ...

RAY SUAREZ:So, this is good news, that they're changing the culture.

MARK THOMPSON:Yes, to go back to what I just said, the math shows that it's going up faster in the unreported realm than in the reported realm.

We see this throughout the military whenever there's a bad problem, be it mental health issues, PTSD, anything that has to be self-reported. Whenever the numbers go up, the Pentagon is always very quick to say, it's because we have removed stigma, we have put signs all over the bases and posts encouraging people to come forward.

And I think there is some truth to that, but essentially it remains a huge problem and they're just getting at a bit of it by reducing the stigma.

RAY SUAREZ:And, at the same time, the arrest of the Air Force's senior officer in charge of getting those numbers down, arrested himself during an accused sexual assault.

MARK THOMPSON:Yes, I mean, that is the problem. That's what stunned everybody I spoke to at the Pentagon over the last couple of days.

I mean, a couple of things about Lt. Col. Krusinski's case. He was picked for that job specifically. And people I talk to suggest, well, he couldn't have been -- you know if someone is right for such a sensitive post. The Air Force put him in that post. A lot of people are asking questions about that now.

And we're just going to have to—the Air Force has asked to take this case away from Arlington County, which is where the Pentagon is located, and prosecute it on their own. We will learn what happens on that score come Thursday.

RAY SUAREZ:You mentioned the female senators. There are also more members of Congress willing to push back on this issue, including a legislative attempt to take the adjudication of these issues out of the chain of the command. What does the Pentagon say in response?

MARK THOMPSON:Well, Sec. Hagel was asked about that today. He doesn't like it. He wants it to stay within the chain of command.

The advocates of change are saying, now, listen, we're not going to take it out of the Pentagon. We're going to keep it in the Pentagon, but it is going to be staffed, for lack of a better word, by a professional force of military sexual trauma advocates, who will be fair, won't be affected, because they won't be in the chain of command of the victim or the accused.

And victims there, advocates believe, will be able to get a fairer shot at their day in court.

RAY SUAREZ:How is this handled in other country's militaries, where they have an even higher percentage of women in the ranks?

MARK THOMPSON:Yes. It doesn't—it seems to be a particularly—particularly nagging problem in the U.S. military, just as gays in the military were a big problem here, and it wasn't a problem anywhere else.

I don't know if it's something in the American psyche or something in the American military, but it's a particular combination that has generated this for a long time.

RAY SUAREZ:Mark Thompson, thanks a lot for being with us.

MARK THOMPSON:You bet.