"The president believes we cannot allow a mere allegation, in this case one from many years ago, to destroy a person's life. However, the president also believes that if these allegations are true, Judge Moore will do the right thing and step aside," Sanders told reporters aboard Air Force One.
Trump put his public backing behind Moore opponent Luther Strange during the Republican runoff but later congratulated the former Alabama Chief Justice on his win and vowed to help him in the Dec. 12 race against Democrat Doug Jones.
The president is currently on a 13-day tour of Asia.
Trump's comments come after a Washington Post report that in 1979, Moore has inappropriate sexual contact with a 14-year-old girl. Several other women, ranging in age from 16 to 18, said Moore tried to date them when he was his 30s.
Moore, now 70, has denied the claims and said they are politically motivated.
Earlier in the day, Vice President Mike Pence said the allegations against Moore were "disturbing."
In a statement provided to NPR, Pence press secretary Alyssa Farah said the vice president found the allegations that Moore had sexual contact with a 14-year old girl when he was in his 30s "disturbing."
"The Vice President found the allegations in the story disturbing and believes, if true, this would disqualify anyone from serving in office," Farah said.
White House counselor Kellyanne Conway urged caution on making an early judgment on Moore.
"We need to listen to both sides, but at the same time, that hypothetical would be disqualifying for anyone in public office," Conway told MSNBC.
A growing number of Republicans have expressed concerns about Moore in the wake of today's story. Among those is Alabama's Senior Senator Richard Shelby.
"If these allegations are true, there is no place for Roy Moore in the United States Senate," he said in a statement.
Moore does have his supporters, however.
On Thursday night, GOP strategist and high-profile Moore backer Steve Bannon said the Post's allegations were similar to the release of "Access Hollywood" videos in 2016 in which Trump was heard making derogatory comments about women.
"By the way, the Bezos Amazon Washington Post that dropped that dime on Donald Trump is the same Bezos Amazon Washington that dropped a dime this afternoon on Judge Roy Moore," Bannon said, referring to Jeff Bezos, Amazon CEO and owner of the Washington Post. "Is that a coincidence? That's what I mean when I say it's the opposition party. It's purely part of the apparatus of the opposition party. It's not a fair and free media anymore ... I don't like it. But I think it's a strange coincidence."
Bannon called it the "politics of self-destruction."
In September, U.S. Rep. Jim Jordan (R-Urbana, Ohio) issued a press release endorsing Moore.
"Roy Moore will be a much-needed conservative voice in the Senate," Jordan said in the release. "I know the voters of Alabama can count on him to adhere to the constitution and always stand for the values and principles that made this nation great, and I am proud to give him my endorsement and support!"
On Friday morning, the Norwalk Reflector reached out to Jordan, asking these questions:
• Do you standby your endorsement and are you still proud of it?
• Please elaborate on the "values and principles" you said Moore will always stand for that made this nation great?
As of 4 p.m. Friday, the Reflector had not received a response from Jordan’s office.
EDITOR’S NOTE: The Norwalk Reflector staff contributed to this story.
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