Sen. John McCain told the top U.S. military chiefs he could not advise women to join the service with a sexual-assault scourge the military has not contained.

"Just last night, a woman came to me and said her daughter wanted to join the military and could I give my unqualified support for her doing so. I could not," the Arizona Republican, a Vietnam veteran and ex-prisoner of war, told the uniformed chiefs of the Army, Navy, Air Force, Marine Corps and Coast Guard at a Senate Armed Services Committee hearing.

"I cannot overstate my disgust and disappointment over continued reports of sexual misconduct in our military," said McCain, who followed his father and grandfather, both four-star admirals, into the Navy.

"We've been talking about this issue for years, and talk is insufficient," McCain said.

The Pentagon estimated in May 26,000 military members experienced "unwanted sexual contact" last year, up from 2011's 19,000 cases.

Yet only a fraction of that number -- 3,374 -- filed sexual-assault reports with military police or prosecutors, the annual Pentagon report said.

Defense officials say most victims don't press charges because they fear retaliation or banishment from their units.

The military chiefs testified Tuesday they were open to new laws requiring tougher action against sex offenders and more support to victims.

But they sharply resisted a bill co-sponsored by a fifth of the Senate that would strip commanders of the authority to oversee criminal sexual-crime cases.

The bill would instead give that authority to military prosecutors.

"Removing commanders, making commanders less responsible, less accountable, will not work," Army Chief of Staff Gen. Raymond Odierno said, explaining the change would undermine the military culture by questioning unit commanders' judgment.

But Sen. Kirsten Gillibrand, D-N.Y., the lead sponsor of the bill, said military leaders had already "lost the trust of the men and women who rely on you that you will actually bring justice in these cases."

In a spirited defense of the bill, Gillibrand said many U.S. allies -- including Britain, Germany, Israel and Australia -- had already "taken the serious crimes out of the chain of command ... [because] not all commanders are objective."

"Not every single commander necessarily wants women in the force, not every single commander believes what a sexual assault is, not every single commander can distinguish between a slap on the ass and a rape because they merge all of these crimes together."

Sen. Claire McCaskill, D-Mo., said earlier nobody at the Defense Department could offer an accurate number of how many women and men in the service were raped because the annual Pentagon report combined criminal attacks and unwanted gazes in the same grouping.

Joint Chiefs of Staff Chairman Army Gen. Martin Dempsey acknowledged "it's probably time to adjust" the broad categorization.

But he said it was created last decade "because we were trying to do the right thing" by considering a minor sexual offense to be serious enough to be included in statistics with rape.

Removing serious sexual crimes from the chain of command is critical, Gillibrand said.

"This has been done before, by our allies, to great effect," she said. "In fact, in Israel, in the last five years, because they prosecuted high-level cases, do you know what has increased by 80 percent? Reporting."