WASHINGTON — In a sign that the White House is increasing its focus on the problem of sexual assault in the military, one of President Obama’s closest advisers met with a group of Congressional lawmakers on Thursday morning to discuss their legislative strategy for addressing the issue.

More than a dozen members of Congress, mostly women from the Senate and House Armed Services Committees, met with Valerie Jarrett, a senior adviser to Mr. Obama, and other administration officials, including Elizabeth Sherwood-Randall, a White House coordinator for defense policy, to discuss the best ways to prevent assault through cultural changes in the military and to improve the judicial process for those who are abused.

“People felt a real sense of urgency,” said Senator Amy Klobuchar, Democrat of Minnesota, who has been working for years on measures to improve the record-keeping of reports of sexual assaults. “They are completely committed to turning this around,” she said of White House staff members.

Of principal interest to many senators is addressing the system for prosecuting violent crimes in the military, in which the person in charge of deciding whether to prosecute, picking the juries and then determining whether to uphold a conviction is a senior commander.

Next week, Senator Kirsten E. Gillibrand, Democrat of New York, will introduce legislation that would give military prosecutors, rather than commanders, the power to decide which cases to try, and would also abolish a commander’s post-trial powers. The measure, which Ms. Gillibrand and Senator Harry Reid of Nevada, the majority leader, aim to place in a broad defense bill next month, is expected to meet fierce resistance from Defense Secretary Chuck Hagel.

According to a Pentagon study made public this week, the military recorded 3,374 sexual assault reports last year, up from 3,192 in 2011, and in a separate survey, thousands more said they had been victims of abuse and not reported it.

The hourlong meeting at the White House also focused on various factors that prevent victims from reporting crimes, including perceived and actual retribution and career damage, and on legislation to combat those problems.

Some of the bills discussed are new, like one introduced this week by Senators Patty Murray, Democrat of Washington, and Kelly Ayotte, Republican of New Hampshire, that would provide victims of sexual assault with a special military lawyer and would change some of the procedures for courts-martial in the case of sexual assault charges.

But older legislation is also getting renewed attention in light of the focus from the White House; Mr. Obama is expected to press the military to accept some changes to the judicial system.

Senator Claire McCaskill, Democrat of Missouri, has proposed legislation that would end a commander’s ability to nullify a jury verdict and require a commander to provide written justification for any decision commuting or lessening a sentence after a guilty verdict in a court-martial.

Ms. Klobuchar, who has passed amendments to guarantee storage of some documents connected with sexual assaults — previously often destroyed — is now sponsoring a bill with Senator Lisa Murkowski, Republican of Alaska, that would expand that record-keeping and remove the requirement that a victim request that retention.