Republican Sen. Susan Collins tweeted that Moore, the GOP nominee, should immediately step aside if the "horrific allegations" published in the Washington Post are true. An Alabama woman told the paper that Moore had sexual contact with her when she was 14 and he was 32.
Moore has denied the allegations.
Senate Majority Leader Mitch McConnell and Colorado Sen. Cory Gardner, who leads the Senate GOP campaign arm, have also said Moore should leave the race if the allegations are true.
Moore faces Democrat Doug Jones in a Dec. 12 special election.