Correction: An earlier version of this story incorrectly reported that Army Gen. Martin E. Dempsey, chairman of the Joint Chiefs of Staff, said he was willing to consider giving military prosecutors, instead of legally untrained commanders, the authority to decide whether to pursue sexual-assault investigations. While Dempsey has said he is open in general to legislative proposals that would change military law to combat sexual assault, he has not said he is willing to consider a bill that would give prosecutors the power to decide whether to investigate cases or take them to trial.

Two senior military officers said for the first time Friday that they were “open” to proposed legislation that would overhaul military law in response to an epidemic of sexual assaults, acknowledging that victims lack faith in commanders to handle the problem.

Army Gen. Martin E. Dempsey, the chairman of the Joint Chiefs of Staff, said some bills in Congress could be "game changers" and that the military would review them closely. Air Force Gen. Mark A. Welsh III, the service’s top commander, said he would be willing to consider giving military prosecutors, instead of legally untrained commanders, authority to decide whether to pursue sexual-assault investigations.

The Pentagon has resisted taking such power away from military commanders. Although neither Dempsey nor Welsh endorsed the proposal, their comments aligned them with Defense Secretary Chuck Hagel, who has said he is willing to discuss it with lawmakers.

With military leaders acknowledging that they are confronting a “crisis” of sexual assaults in the ranks, pressure is building in Congress to pass major legislation to address the issue.

A bipartisan group of lawmakers announced Thursday that they support a bill from Sen. Kirsten Gillibrand (D-N.Y.) that would force the most significant changes in military law in 30 years by giving prosecutors, instead of unit commanders, the power to open investigations into serious crimes and send the cases to trial.

Some influential lawmakers on the House and Senate armed services committees remain cool to the idea, saying it is important to preserve commanders’ authority. But the proposal has gained momentum with a string of recent sex-crime scandals and other embarrassing disclosures.

In a news conference Friday, Welsh, the Air Force’s chief of staff, said “all options should be on the table” and that “I personally am open” to a plan that would give prosecutors the authority to pursue sexual-assault cases.

Ten days earlier, he testified before the Senate Armed Services Committee that he was opposed to the idea. “I feel very strongly that that’s in the commander’s purview for a reason,” he said.

On Friday, Welsh said that combatting sex crimes was his top priority and that he personally reviews each report of sexual assault in the service; 792 cases were reported last year.

He added that the problem is often rooted in alcohol abuse and a basic 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,” Welsh said. “In many of the cases, it’s friends who get together. Typically alcohol is involved. And at some point during the evening, if it’s a man on a woman, the man basically just shows a lack of respect for the woman, who is incapacitated, and commits a crime. It’s not a mistake. It's not bad behavior. It’s a crime.”

Among the armed services, the Air Force has the highest percentage of women — about 19 percent.Welsh also apologized for his comments last week when he partially attributed the rise in sexual assaults in the military to a “hook-up culture” among young people. “As far as victims taking what I said as blaming them, I am sorry about that,” he said.

In general, Welsh and other Pentagon leaders said they were scrambling for solutions to the broader problem of sexual assault.

At a separate news conference, Hagel said some have questioned why he hasn’t fired anyone to make a statement about accountability. He said the problem was broader than that.

“Who are you going to fire?” he asked.