WASHINGTON — Sen. Kirsten Gillibrand’s push to overhaul the military’s justice system has gained crucial support in the House, but is facing renewed resistance from the Pentagon.

This week, Speaker Nancy Pelosi vowed to bring the legislation up for a vote in the House, where she said it will pass.

“This is a challenge that we have. It is long overdue that it is addressed,” she said at a press event Wednesday.

For weeks, Gillibrand, a Democrat representing New York, has made nearly daily trips to the Senate floor, calling unsuccessfully for an expedited vote on her bill in that chamber.

“We do not have time to delay,” she said during one appearance in the past week.

The legislation would put decisions about how to handle serious crimes like murder and rape in the hands of independent military prosecutors, taking those decisions away from military commanders.

“When the commanders say, ‘We’ve got this ma’am, we’ve got this,’ they don’t have it,” she said.

Her bill has more than 60 supporters in the Senate — Democrats and Republicans alike.

However, a key Democrat — Sen. Jack Reed, the chairman of the Senate Armed Services Committee — is blocking a quick vote, wanting the legislation to go through the traditional committee process instead.

Top military leaders are also pushing back.

In newly released letters sent to the top Republican on the Senate Armed Services Committee, members of the Joint Chiefs of Staff raised concerns about the large variety of crimes that would be taken out of the chain of command under the legislation — beyond just sex crimes.

In his letter, Chairman Mark Milley wrote, “It is my professional opinion that removing commanders from prosecution decisions, process, and accountability may have an adverse effect on readiness, mission accomplishment, good order and discipline, justice, unit cohesion, trust, and loyalty between commanders and those they lead.”

In the letter, Milley did say he was “open-minded” about how to handle sexual assault cases.

Asked about the letters, Gillibrand said military leaders have been fighting reforms since the beginning.

“They don’t want to do anything. So if I was to put it in military terms, they have retreated to just sexual assault,” she said.

Earlier this week, Defense Secretary Lloyd Austin backed removing sex-related crimes from the chain of command. Gillibrand called that a huge step forward, but argued they must go further.