Senate Majority Leader Harry Reid, D-Nev., announced Tuesday he will support legislation from Sen. Kirsten Gillibrand to remove prosecutions of serious crimes, including sexual assault, from the military chain of command.

Within the past few weeks, Reid met with both Gillibrand and Sen. Claire McCaskill, D-Mo., who has been advocating changes pushed by the Armed Services Committee. Reid also met with various outside groups lobbying on the issue.

The majority leader decided late last week to break from the position of Senate Armed Services Chairman Carl Levin and military top brass to support the Gillibrand bill. White House spokesman Jay Carney declined to state President Barack Obama’s preference on the issue when asked Tuesday, and the administration’s detailed and wide-ranging statement of policy on this year’s defense authorization released Monday stated only that it “commends the Committee for working to offer stronger protections for sexual assault victims.”

“I’m going to support Gillibrand and Sen. Levin knows that,” Reid told reporters after Democrats’ weekly caucus luncheon.

Gillibrand said earlier Tuesday that she had the support of more than half of the Senate for her measure, which will need to clear a 60-vote threshold in order to be adopted. The New York Democrat, who has made sexual assault in the military her signature issue, said she planned to speak to all of the undecided senators on the bill on Tuesday. A vote on her plan could come as early as Wednesday.