Roy Moore -- a former state judge and Christian evangelical whose defence of a Ten Commandments display brought him national attention -- added he had "never engaged in sexual misconduct."
The issue has reverberated through Washington weeks ahead of a crucial Senate election in which the conservative Republican party is hoping to hold on to its slim 52-48 seat majority.
Four women, speaking on the record, told The Washington Post that Moore pursued them when they were 18 or younger, while he was in his early thirties working as an assistant district attorney.
Moore guided her to touch him through his underwear, she said.
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"I wasn't ready for that," Corfman told the Post.
Now 70, the anti-establishment conservative faces Democrat Doug Jones in a special Senate election December 12 to replace Jeff Sessions, who became US attorney general earlier this year.
"I have never engaged in sexual misconduct," he said in a statement issued yesterday that went beyond his campaign's earlier simple denial.
"False allegations are gravely serious and will have a profound consequence on those who are truly harassed or molested," he added.
He also appeared on conservative media personality Sean Hannity's radio show to rebut the story.
Asked whether he remembered dating women in their teens when he was in his 30s, he said: "Not generally no."
He added: "I don't remember that, or dating any girl without the permission of her mother."
Earlier, President Donald Trump issued a statement that appeared to equivocate on the matter, saying Moore should step aside if the claims proved true, while adding that a mere allegation should not destroy the Alabama politician's life.
"However, the president also believes that if these allegations are true, Judge Moore will do the right thing and step aside," she said.
The accusations by the four women reverberated through Washington, with many traditional Republicans withdrawing their support for Moore -- though he has received considerable support in his native Alabama and from former Trump advisor Stephen Bannon.
Senator John McCain, the 2008 Republican presidential nominee, declared the allegations "disqualifying" for Moore and called on him to immediately leave the race.
But in Alabama, state auditor Jim Zeigler brushed off the allegations.
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