Corrected 8:19 p.m. | The Senate on Thursday voted to limit debate on taking up a bipartisan bill that would repeal two military authorizations for use of force against Iraq, setting up a likely vote on passage next week, 20 years after the March 19, 2003, attack on Baghdad.

The vote, 68-27, in favor of cloture on a motion to proceed to legislation that would repeal the 2002 Iraq AUMF and the 1991 Gulf War AUMF represented years of painstaking work on the part of sponsor Sen. Tim Kaine, D-Va., and co-sponsor Sen. Todd Young, R-Ind., to convince enough colleagues, particularly Republicans, that U.S. national security wouldn’t be harmed by ending the authorities, and that the rule of law and the balance of powers between Congress and the presidency would be strengthened.

“Now almost 20 years to the day that U.S. military operations began in Iraq, the United States Senate begins the process of repealing the Iraq AUMFs … putting the final remnants of those conflicts squarely behind us,” Senate Majority Leader Charles E. Schumer, D-N.Y., said in a Thursday floor speech. “The United States, the nation of Iraq and the entire world have changed dramatically since 2002 and it’s time the laws on the books catch up with these changes.”

The White House issued a statement of support for the legislation on Thursday, noting there are no ongoing military operations that rely primarily or at all on the two Iraq AUMFs.

“Repeal of these authorizations would have no impact on current U.S. military operations and would support this administration’s commitment to a strong and comprehensive relationship with our Iraqi partners,” the statement of administration policy said. “That partnership, which includes cooperation with the Iraqi Security Forces, continues at the invitation of the government of Iraq in an advise, assist, and enable role.”

Ahead of expected Senate passage next week, Schumer said he was anticipating votes on multiple amendments.

Looking ahead to the measure going to the House, Kaine said Wednesday that he hoped a strong Senate majority for passage might prompt House Republican leaders to bring the measure up for a stand-alone vote. House efforts to repeal the 2002 AUMF have usually been through amendments to the annual defense policy bill.

“The more convincing the Senate vote, the more likely we can have the momentum to take it up stand-alone on the House side,” Kaine said. “So we’ll get through the Senate piece of it first, try to get as big a vote as we can, then we’ll go start working on the House.”

This report has been corrected to reflect that the cloture vote was on the motion to proceed.