WASHINGTON – An ambitious, bipartisan effort to overhaul the military justice system and stanch the increasing number of sexual assaults gained crucial support from conservatives Tuesday, setting up a showdown with the Pentagon’s top brass.

Sen. Rand Paul, R-Ky., announced his backing for legislation sponsored by Sen. Kirsten Gillibrand, D-N.Y., that would remove commanders from the process of deciding whether serious crimes, including sexual misconduct cases, go to trial. That judgment would rest instead with seasoned trial lawyers who have prosecutorial experience and hold the rank of colonel or above.

“There’s no reason why conservatives shouldn’t support this,” Paul told reporters at a Capitol Hill news conference with other Republicans and Democrats who support the measure.

A third of the Senate — 33 lawmakers — favor Gillibrand’s effort that she will try to attach to a sweeping defense policy bill, perhaps as soon as this month. She faces opposition from Senate Armed Services Committee Chairman Carl Levin, D-Mich., who — echoing the Joint Chiefs of Staff — wants to keep commanders involved in deciding whether to prosecute sexual assault cases.

“If you remove the chain of command, you are taking away the club that they need to change the culture,” Levin told reporters Tuesday at a breakfast discussion hosted by The Christian Science Monitor. The club, he said, is the ability of commanders to prosecute people.

“It’s commanders who make it work,” he said. “They give orders.”

Military leaders have argued that removing the decision from their purview would undercut the ability of officers to maintain good order and discipline in their units.

The Pentagon estimated in a recent report that as many as 26,000 military members may have been sexually assaulted last year, up from an estimated 19,000 assaults in 2011, based on an anonymous survey of military personnel.

Backers of Gillibrand’s legislation insist that leaving the decisions with the commanders has failed to stop a crisis within the military ranks.

“The status quo is not working and we need to shake it up,” said Sen. Charles Grassley, R-Iowa.