WASHINGTON — A bipartisan effort to stanch the increasing number of military 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.

A third of the Senate favor Gillibrand’s effort that she will try to attach to a defense policy bill. She faces opposition from Senate Armed Services Committee Chairman Carl Levin, D-Mich., who wants to keep commanders involved.

“If you remove the chain of command, you are taking away the club that they need to change the culture,” Levin told reporters Tuesday.

The Pentagon estimated in a 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 insisted that leaving the decisions with the commanders has failed to stop a crisis.

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