Alabama GOP Senate candidate Roy Moore said Friday that allegations that he had sexual contact with underage girls in the late 1970s and early 1980s was "completely false" and "based on a lie supported by innuendo."

Moore made the comments in an extensive new written statement and in an interview on the "Sean Hannity Radio Show."

On Thursday, a Washington Post report alleged that Moore initiated sexual contact with a 14-year-old girl in 1979, when he was a 32-year-old assistant district attorney in Gadsden, Ala. The report also included claims by three other women that Moore asked them out on dates -- and in two cases, kissed them -- when they were between the ages of 16 and 18. The legal age of consent in Alabama is 16.

"I have never provided alcohol to minors, and I have never engaged in sexual misconduct," said Moore in his statement, referencing a claim by one of the women that he gave her wine when she was below Alabama's legal drinking age, which is 19.

"As a father of a daughter and a grandfather of five granddaughters," Moore went on. "I condemn the actions of any man who engages in sexual misconduct not just against minors but against any woman."

In the radio interview with Hannity, Moore denied ever knowing Leigh Corfman, who told the Post he made sexual advances toward her when she was 14. However, he did not deny dating teenagers as young as 16.

"You understand this was 40 years ago," Moore said. "And after my return from the military, I dated a lot of young ladies."

When asked by Hannity if he dated teenagers when he was in his 30s, Moore said "It would have been out of my customary behavior," and added that he didn't "remember dating any girl without the permission of her mother."

In his statement, Moore implored "the Washington Post, and everyone involved [in the story], to tell the truth." But on the radio, Moore said he was "sure in the next four weeks, they're gonna come out with another article." He also said that his campaign had "some evidence of collusion," but did not elaborate.

"I trust that the people of Alabama, who know my record after 40 years of public service, will vouch for my character and commitment to the rule of law," Moore's statement concluded.

The allegations have caused an outcry from national Republican leaders, who have called on Moore to drop out of the race if the allegations are proven true. On Friday, the Senate GOP's campaign arm formally ended its fundraising agreement with Moore.

The GOP's 2012 presidential nominee Mitt Romney condemned his colleagues' caveat -- only if the allegations are true.

"Innocent until proven guilty is for criminal convictions, not elections. I believe Leigh Corfman," Romney said. "Her account is too serious to ignore. Moore is unfit for office and should step aside."

However, the former state Supreme Court justice has emphatically refused to leave the race, telling Hannity if candidates step aside due to accusations, "you might as well not run, because when you run you're going to get allegations."

Despite the allegations, Moore also has the support of several Republican officials in Alabama.

"Humphrey Bogart started dating Lauren Bacall when she was a teenager," said state Auditor Jim Ziegler, referring to the then-19-year-old actress.

Paul Reynolds, Alabama's Republican National Committeeman, called it "a firestorm designed to shipwreck a campaign in Alabama. I think it's sinister."

Fox News' Alex Pappas and the Associated Press contributed to this report.