The support from the Senate's top Democrat in a heated intraparty debate came as the Senate prepared to vote on the contentious bill as early as Wednesday.
Reid, D-Nev., told reporters after a weekly lunch among Senate Democrats he told Senate Armed Services Committee Chairman Carl Levin, D-Mich., he backed the measure by Gillibrand, D-N.Y.
Gillibrand's proposed Military Justice Improvement Act would give military prosecutors rather than commanders the power to decide which sexual assaults to try. The goal is to increase the number of people who report cases without fear of retaliation, Gillibrand says.
Reid is the 50th senator to say publicly he would vote yes on Gillibrand's amendment to a broader defense-authorization bill.
Levin is the co-author with Sen. Claire McCaskill, D-Mo., of a bill that would keep military commanders as part of the effort to combat sexual assaults but would strip them of their ability to overturn convictions.
The McCaskill-Levin bill would also require a senior military officer to review decisions by commanders who decline to prosecute sexual assault cases. And it would remove statutes of limitations for court-martial proceedings on sexual assaults.
The Pentagon says sexual-assault prosecutions must stay with military commanders to maintain good order and discipline.
Female senators from both sides of the aisle said Tuesday they supported Gillibrand's bill and spoke out against sexual assault in the military.
"When you join the military and you face the enemy, you shouldn't have to fear the enemy within," Sen. Barbara Mikulski, D-Md., was quoted by The Wall Street Journal as saying.
"We're not going to let this go. This is not going to be something where we pass these reforms and that's the end of the story," said Sen. Kelly Ayotte, R-N.H.
McCaskill said on the Senate floor Tuesday she wanted to make sure the focus on this policy disagreement didn't take away from the broader effort to address sexual assaults in the armed services.
"I would be less than candid if I didn't say it has been frustrating to have one policy difference dominate the discussion of this issue over the previous few weeks without anyone even realizing the historic reforms that are contained in this bill," she said of her measure.
Senate Minority Leader Mitch McConnell, R-Ky., told reporters Tuesday he hadn't decided which bill he would support. Senate Majority Whip Richard Durbin of Illinois, the second-highest Senate Democrat, told the Journal through an aide he too hadn't reached a decision.
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