Moore, a former judge and the Republican nominee for a vacant Senate seat in Alabama, has denied explosive allegations from four women that he pursued them when they were 18 or younger while he was in his 30s. One woman said she was just 14 at the time.
"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," White House press secretary Sarah Huckabee Sanders told reporters aboard Air Force One before Trump arrived in Vietnam to attend an Asia-Pacific summit.
"However, the president also believes that if these allegations are true, Judge Moore will do the right thing and step aside."
The four women were interviewed on the record by The Washington Post, alleging a range of incidents while Moore was working as an assistant district attorney in Alabama.
According to the Post, Leigh Corfman, now 53, said when she was 14 Moore took her into his house in the woods near Gadsden, Alabama, removed her shirt and pants, and fondled her over her bra and underpants.
The allegations have sent shockwaves through Washington, with several high-profile Republicans urging the married father-of-four to quit the Senate race if the claims are true.
Senator John McCain, the 2008 Republican presidential nominee, immediately declared the allegations "disqualifying" for Moore.
Moore, 70, denies the allegations. His campaign team called the Post story "fake news."
Considered an anti-establishment conservative, Moore will face Democrat Doug Jones in a special Senate election December 12 to replace Jeff Sessions, who is now US attorney general.
Experts have told US media that Alabama's Republican Party or Moore himself could withdraw his name from consideration.
However, Alabama law prohibits the replacement of a candidate up to 76 days before the election, meaning Moore's name will likely be on the ballot when Alabamians vote next month.
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