Updated at 4:05 p.m. ET

Roy Moore, the Republican nominee for the open Senate seat in Alabama, is facing an accusation from a woman who says that he initiated sexual contact when she was 14 years old and he was a 32-year-old assistant district attorney.

The Washington Post published a story Thursday documenting the accusations by Leigh Corfman, who spoke on the record to the paper along with her mother, as well as three other women who say Moore pursued romantic involvement when they were between the ages of 16 and 18 and he was in his early 30s. The age of consent in Alabama is 16.

The allegations threaten to roil the special Senate election next month where the former Alabama chief justice is set to face former U.S. Attorney Doug Jones. GOP leaders have already said that if the allegations are true, Moore should step aside.

Moore, now 70, denied the allegations in a statement to the Post.

"These allegations are completely false and are a desperate political attack by the National Democrat Party and the Washington Post on this campaign," he said.

In a statement, Moore's campaign chairman, Bill Armistead, said, "Judge Roy Moore has endured the most outlandish attacks on any candidate in the modern political arena, but this story in today's Washington Post alleging sexual impropriety takes the cake. National liberal organizations know their chosen candidate Doug Jones is in a death spiral, and this is their last ditch Hail Mary."

In September, Moore defeated appointed Sen. Luther Strange in the Republican primary runoff for the open U.S. Senate seat vacated by Attorney General Jeff Sessions.

Senate Majority Leader Mitch McConnell said in a statement, "If these allegations are true, he must step aside."

McConnell and his allied superPAC heavily backed Strange in the GOP primary, along with President Trump. Meanwhile, Moore was endorsed by Trump's former chief strategist Steve Bannon, who painted Strange as a creature of the Washington "swamp." Bannon touted Strange's loss as the first casualty in his war against the GOP establishment and his plans to primary other incumbents.

NPR has asked Bannon for comment on Moore and has not yet heard back.

National Republican Senatorial Committee Chairman Cory Gardner echoed McConnell's call for Moore to withdraw if the allegations are true, calling them "deeply troubling."

Per Alabama law, it is too late for Moore's name to be taken off the ballot.

The allegations throw a wrench into the race, which Republicans were already mildly fretting about even before the Post report, given Moore's controversial past.

Moore rose to fame after he refused to remove a monument of the Ten Commandments he'd had placed in the rotunda of the Alabama Judicial Building. That led to his being removed from the bench the first time. He was subsequently elected again to the bench but later suspended after ordering state judges to defy the Supreme Court's 2015 decision that legalized same-sex marriage.

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