(Reuters) - A woman has accused Roy Moore, the Republican nominee for the U.S. Senate in Alabama, of initiating a sexual encounter with her when she was 14 years old and he was 32, the Washington Post reported on Thursday, prompting top Republicans to say he should step aside if the allegations prove true. Moore, 70, the state’s former chief judge, vehemently denied the allegations, calling them “completely false and a desperate political attack.” U.S. President Donald Trump would want Moore to step aside if the allegations against him are true, White House press secretary Sarah Sanders said on Friday. “Like most Americans, the president believes we cannot allow a mere allegation, in this case one from many years ago, to destroy a person’s life,” Sanders said. “However, the president also believes that if these allegations are true, Judge Moore will do the right thing and step aside,” she said, as Trump arrived in Vietnam on his 12-day Asia tour.   In a series of Twitter posts later in the day, Moore cast the published allegations against him part of a bid to “silence and shut up Christian conservatives like you and me,” adding “I will NEVER GIVE UP the fight!” Senate Republican leader Mitch McConnell, working with a slim 52-48 majority, called on Moore to drop out of the race “if these allegations are true.” Several other Republicans, including Texas Senators John Cornyn and Ted Cruz, and Utah Senator Mike Lee, all of whom endorsed Moore, echoed that sentiment. At least two Republican senators, John McCain of Arizona and John Thune of South Dakota, said Moore should step aside immediately, with McCain calling the accusations “deeply disturbing and disqualifying.” Leigh Corfman, now 53, told the Post she met Moore at a courthouse in 1979 when Moore offered to keep her company on a bench outside of a hearing room while her mother was inside for child custody proceeding. Moore, at the time an assistant district attorney, asked for the girl’s phone number and days later took her to his house, where they engaged in sexual activity before she asked to be taken home, Corfman said. The story also quoted three other women who said Moore dated them when they were between 16 and 18 years of age and he was in his early 30s, though none said they had sexual contact with Moore.  Reuters was unable to independently confirm the allegations. The Moore campaign accused the Post of colluding with Democrats to tarnish his reputation with false accusations.  The Post said none of the women had donated to or worked for Moore’s Democratic opponent, Doug Jones, or for his Republican primary rivals, and that Corfman said she had voted for Republicans in the past three presidential elections, including for Donald Trump in 2016.  Moore has consistently led in polls over Jones. He was considered a heavy favorite in deeply Republican Alabama in the Dec. 12 special election to fill the seat of U.S. Attorney General Jeff Sessions. It remains to be see whether Thursday’s allegations can buoy Jones’ long-shot bid, which would represent a major upset for Democrats and narrow Republicans’ current edge in the Senate.  Jones’ campaign did not immediately respond to a request for comment on the Post story. No matter what happens, Moore will remain on the ballot on Dec. 12 since a candidate’s name cannot be removed within 76 days of the election, according to the office of Alabama’s secretary of state. If, however, the state party tells election officials that it wants to withdraw its nominee, or if Moore himself decided to do so, election officials would not certify any votes cast for Moore. Write-in candidates are also allowed under state law. Alabama political strategist David Mowery, who has worked for candidates of both parties, said the chance of Moore bowing out of the race was “less than zero,” and that it was almost as improbable for state party officials to abandon him in favor of a last-minute write-in candidate. Mowery cited Moore’s overwhelming popularity with Alabama’s Republican voters, who he said would tend to distrust allegations published in the Post. Nevertheless, he said Democrats would seize on the scandal to boost fund-raising. Moore, who has made his moral and religious beliefs the heart of his pitch to voters, prevailed over several Republican opponents in a closely contested primary that saw Trump, McConnell and most Senate Republicans support the incumbent who had been appointed to Sessions’ seat, Luther Strange. The race exposed rifts between the Republican Party’s conservative base and its Washington-based establishment. Moore’s candidacy was heavily promoted by former Trump strategist Steve Bannon, who has vowed to support grassroots challengers next year to take on Republican incumbents. On several occasions, Moore has made controversial statements and taken positions that have cost him his job. He has condemned homosexuality and said he believes some U.S. communities are living under Islamic religious law. He first became a national figure in the early 2000s, when he lost his position as Alabama chief justice after refusing a court order to remove a Ten Commandments monument from outside the courthouse. After winning his position back in 2012, he was again forced out after defying the U.S. Supreme Court decision legalizing gay marriage by ordering probate judges not to give marriage licenses to same-sex couples. On his Senate campaign website, Moore said he was suspended “for upholding the sanctity of marriage as between one man and one woman.” 