Senate leadership will move ahead this week with a full-chamber vote on Air Force Gen. John Hyten’s nomination to become the next vice chairman of the Joint Chiefs, potentially ending months of controversy surrounding his promotion.

Senate Majority Leader Mitch McConnell, R-Ky., said Tuesday that before the end of the week “we’ll have confirmed our next vice chairman of the Joint Chiefs,” voicing his own support for Hyten’s nomination. The current head of U.S. Strategic Command was advanced by the Senate Armed Services Committee in a 20-7 vote in July.

Hyten’s nomination, announced in April, has been slowed for months over allegations of sexual harassment and assault of a former aide. Hyten has publicly denied the charges.

Air Force officials have backed him after an internal investigation turned up insufficient evidence for criminal charges, and released parts of their review of the case which cast doubt on his accuser’s credibility.

During a confirmation hearing in July, several Republicans from the Senate Armed Services Committee praised Hyten as an exemplary nominee and attacked that accuser — Army Col. Kathryn Spletstoser — as a toxic leader who has made false accusations in the past.

In an opinion piece in Military Times last month, Spletstoser said she has been “publicly smeared” by military officials desperate to cover up problems in the ranks.

“Confirming Gen. Hyten for a promotion instead of subjecting him to disciplinary action for misconduct diminishes us all,” she wrote.

This weekend, attorneys for Spletstoser distributed a 14-page memo among Senate staffers on her allegations and dealings with Air Force officials. They also noted that Spletstoser was not invited to testify before the committee in public, although committee members did speak with her in private ahead of the confirmation hearing.

Sen. Jim Inhofe, R-Okla., has said since July that he hoped Republican leaders would move forward with the nomination, saying he was satisfied that his committee conducted a thorough review of the allegations and that Hyten is well-qualified for the post.

No specific day for the vote was set, but the Senate is expected to break for a two-week fall recess starting Thursday afternoon. McConnell said he hopes to clear a handful of nominations by then, as well as pass a budget extension bill to keep government operations running past Oct. 1.