In The Washington Post report, one woman accused Moore of driving her to his house in the woods, stripping down to his underwear, stripping her down to her underwear and trying to touch her.
Mr. Moore's candidacy had already anxious party leaders who had embraced the controversial former state Supreme Court justice despite his long record of incendiary comments about gays, Muslims and African-Americans, to protect the Senate seat once held by Attorney General Jeff Sessions. "Even the Washington Post report says that he never had sexual intercourse with any of the girls".
Senate Majority Leader Mitch McConnell said that if the allegation is true, Moore "must step aside".
Mr Moore, a populist former chief justice in the state, has been widely expected to defeat a Democratic rival, Doug Jones, in a December election for the open seat left by US Attorney General Jeff Sessions. "He touched her over her bra and underpants, she says, and guided her hand to touch him over his underwear".
Moore's campaign responded on Thursday afternoon, denying the report.
Moore came under fire for his extremely conservative positions and statements made over the years, including a 2006 suggestion that Minnesota Rep. Keith Ellison, the first Muslim elected to Congress, shouldn't be seated because "Islamic law is simply incompatible with our law", and his contention that homosexuality should be illegal.
Corfman, then 14, told the newspaper that Moore picked her up around the corner from her home and took her to his place where he told her she was pretty and began kissing her.
Days later, Corfman said, Moore drove her to his home, complimented her appearance, and kissed her.More news: IPhone glitch creating typos for users
The Washington Post article alleges that Mr Moore, who was then an assistant district attorney, struck up a conversation with Ms Corfman when she was 14.
'This garbage is the very definition of fake news, ' according to the statement. "[Luther] Strange", he said, referring to the temporarily-appointed senator whom Moore defeated in the GOP primary.
The Post says that three other women have come forward charging that Moore pursued them when they were between the ages of 16 and 18 and he was in his 30s.
The legal age of consent in Alabama in 1979, and now, is 16.
Moore prevailed over several Republican opponents in a closely contested primary that saw U.S. President Donald Trump, McConnell and most establishment Republicans back the incumbent, Luther Strange. She says she thought about going public as early as 2000, when Moore was running his first campaign for state Supreme Court.
Asked whether Moore should represent his state, Alabama's senior senator, Richard Shelby, replied: "I supported Senator Strange - you all know that".
"If that's true, he wouldn't belong in the Senate", said Sen.
"If they are true, then he should seriously think about stepping aside", he said.
In fact, just two days ago, the Foundation for Moral Law sent a retraction demand to the Post for the false stories they wrote about the Judge's work and compensation.