Moore -- a former state supreme court judge running a tight race against a Democratic lawyer -- denies any wrongdoing, calling the allegations "absolutely false."
But Beverly Young Nelson claimed the now 70-year-old grandfather sexually assaulted her when she was a 16-year-old waitress and he was a county district attorney twice her age around January 1978.
Nelson, who is now a 55-year-old businesswoman in Alabama, told reporters in New York yesterday that Moore, a regular in the restaurant where she worked, one night offered to drive her home after she finished her shift.
Moore then groped her and squeezed her neck, attempting to force her head onto his crotch, she said, reading from a prepared statement alongside celebrity lawyer Gloria Allred, who has represented women who accused felled Hollywood mogul Harvey Weinstein of sexual assault.
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"I was terrified. He was also trying to pull my shirt off. I thought that he was going to rape me. I was twisting and struggling and begging him to stop," Nelson said, speaking through tears.
Nelson said she was motivated to speak out after four other women told The Washington Post that Moore also pursued them in their teens, while he was in his early 30s working as an assistant district attorney.
"I can tell you without hesitation this is absolutely false," Moore said, speaking alongside his wife, who expressed support.
"I never did what she said I did. I don't even know the woman. I don't know anything about her. I don't even know where the restaurant is or was," he told reporters, declining to take any questions.
But he faced mounting calls late yesterday to quit the tight race with Democrat Doug Jones as Republicans seek to hold on to their slim 52-48 majority in the Senate and replace Jeff Sessions, now US attorney general.
The Senate's top Republican Mitch McConnell said he believed Moore's accusers and urged the anti-establishment conservative -- who is far to the right of his own party -- to "step aside" from the December 12 election.
Senator Jeff Flake, a Republican, said he would rather vote for a Democrat than for Moore, and agreed on calls to expel him should he win.
Under Alabama law, it is too late to have Moore's name taken off the ballot, but some Republicans have discussed putting forth another candidate voters could write in manually on their ballot.
The number two Senate Republican, John Cornyn, withdrew his endorsement of Moore, calling the accusations "disturbing and, if true, disqualifying."
Lindsey Graham, the prominent Republican senator from South Carolina, followed suit, tweeting that Moore "would be doing himself, the state, the GOP, and the country a service by stepping aside."
But some still expressed support. Alabama Representative Mo Brooks said he backed Moore because his Democratic rival will "vote wrong."
"Doug Jones will vote wrong on each of those issues... Roy Moore will vote right; that's why I'm voting for Roy Moore."
Allred left open the possibility that other accusers may come forward, refusing to comment when asked if other women had contacted her about Moore.
The accusations have inflamed national debate about sexual harassment in the wake of the Weinstein scandal, as women flood social media with photographs of themselves at 14 -- all braces and schoolgirl innocence -- to raise alarm over the issue of consent.
Nelson batted aside any suggestion that she was motivated by politics.
"My husband and I supported Donald Trump for president," she said. "This has nothing whatsoever to do with Republicans or Democrats.
"Mr Moore attacked me when I was a child. I did nothing to deserve this sexual attack. I was frightened by his position and his power," she said.
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