Senate Majority Leader Harry Reid will try to bring to the floor next week a defense authorization measure that contains an amendment to repeal the military’s ban on openly gay service members.

The Nevada Democrat told Minority Leader Mitch McConnell (R-Ky.) that he would bring up the defense measure next week, Armed Services Chairman Carl Levin (D-Mich.) said Monday. It was unclear if the two reached a time agreement or whether the bill could come to the floor without procedural hurdles.

“I do believe from staff it’s his intent to move to it next week,” Levin told reporters.

Levin, who tried to bring up the defense measure before the Senate adjourned for recess last month, said he was not sure whether Democrats would be able to bring up the bill without procedural hurdles. Republicans, led by Arizona Sen. John McCain, widely oppose the language repealing “don’t ask, don’t tell,” but they are not likely to have 60 votes to sustain a filibuster. Still, Reid may have to file a cloture motion to tee up the bill for floor action next week.

McCain has maintained that Congress should not act until after the Pentagon has completed a yearlong review of the effects a repeal would have on military forces.

“Senator McCain strongly believes in the importance of completing the comprehensive review of the ‘Don’t Ask, Don’t Tell’ law prior to taking any legislative action to repeal the policy,” spokeswoman Brooke Buchanan said in an e-mail. “As all four Service Chiefs have stated, we should not short circuit the ongoing Pentagon review and thereby deny our men and women in uniform a chance to have their voices heard on an important issue that affects them and their service.”

The legislative push comes just days after a federal judge in Southern California ruled that the military’s ban is unconstitutional. Activists including the Human Rights Campaign and the Servicemembers Legal Defense Network said the court decision underscored the need for Congress to approve a repeal. They demanded the Senate act on the defense bill before leaving town next month for the midterm elections, fearing a more challenging political environment during the lame-duck session.

The defense authorization typically enjoys broad bipartisan support, but this year it has been mired in the DADT debate. The bill is also usually on the floor for a few weeks before it receives final approval, so Reid’s attempt to bring up the measure next week could trip up his fall agenda.