The article in Thursday's Washington Post contains allegations from a woman who said Moore kissed her and touched her while she was in her underwear in 1979.
Republican Sen. Cory Gardner of Colorado says, "The allegations against Alabama Senate candidate Roy Moore are deeply troubling".
"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", read a statement from Moore's campaign, calling the story a "last ditch Hail Mary" by liberal organizations backing his Democratic Senate rival Doug Jones.
She called for Senator Luther Strange, who was appointed to fill Mr. Sessions' seat but lost to Mr. Moore in a bitterly contested Republican runoff in September, to run as a write-in. On a second visit, he took off her shirt and trousers and removed his clothes except for his underwear before touching her over her bra and underpants, Corfman told the Post.
The Post's Michael Scherer followed Senate candidate Roy Moore (R) in the final days of his primary campaign against Sen.
Corfman said she chose to come forward this time because she couldn't "let this continue".
Wendy Miller told the Washington Post that Moore first approached her when she was 14 years old, and asked her on dates when she was 16 years old.
The two did not have intercourse, Corfman told the Post.
But Alabama election law appears to indicate, with little ambiguity, that the deadline has passed for candidates to be replaced on the ballot.
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Her use of offshore tax havens is likely to generate criticism from activists seeking to abolish the monarchy in favor of a republic.
Sen. Jeff Flake (R-Ariz.) echoed the majority leaders comments tweeting, "If there is any shred of truth to the allegations against Roy Moore, he should step aside immediately".
Four women have told the Washington Post that Alabama Senate candidate Roy Moore pursued them when they were teenagers - between the ages of 14 and 18 - and he was in his 30s.
Former White House chief strategist backed Moore in the GOP primary.
The women, who spoke on the record to the Post, said Moore asked them out on dates while serving as an assistant district attorney in Gadsden, Alabama.
Moore was removed as chief justice of the Alabama Supreme Court twice - once for refusing to remove a monument of the Ten Commandments he had installed in the state courthouse, later for barring clerks from issuing same-sex marriage certificates following the U.S. Supreme Court ruling that legalized them.
Reaction after the Post story was published online was swift and severe.
Debbie Wesson Gibson told the Washington Post that Moore asked her out when she was 17 years old and that they went on several dates but their physical involvement was limited to kissing.
It's unclear what will happen to Moore's candidacy if he seeks to pull out before the special election against Democrat Doug Jones.
Moore's resignation is made all the more unlikely by the fact that he's publicly called these allegations "fake news", in an attempt to throw doubt on the women's claims. She says they sat and talked. Although one told the Post that Moore had ordered her cocktails when she was below the legal drinking age, there were no other accusations of illegal behavior.