"He has said that he thinks that the voters of Alabama should decide", Mulvaney told Andrea Mitchell on Sunday's "Meet The Press".
Asked if she is proud to vote for Moore, Ivey didn't directly address the twice-ousted former state Supreme Court chief justice.
In the wake of several women saying Moore sexually harassed or assaulted them when they were teenagers, the Republican National Committee has pulled support for him, and a number of prominent GOP members have called on Moore to step aside for the December 12 special election.
Ivey made her comments on the same day that Moore's wife Kayla Moore said that her husband would not bow out of the contest, despite Senate Republican leaders vigorously urging him to do so.
Moore's campaign has painted the allegations as politically motivated.
Moore is accused of sexual misconduct with numerous women, including underage girls.
Democratic nominee Doug Jones, who campaigned in the southeastern part of the state on Friday, criticized Ivey's justification for supporting Moore.
Moore has pledged to fight the accusations against him as the state GOP in Alabama reaffirmed its support for the embattled candidate.
The accusations sent a shockwave through the Senate race in Alabama, where Republicans typically have a lock on statewide election.
"The credibility of evangelicals is being harmed by the perception that evangelicals don't care about victims but instead just care about political power", said Ed Stetzer, who chairs the Billy Graham Center at Wheaton College.
When asked by a reporter why the allegations against Trump don't require an investigation but Franken's do, Sanders said, "the American people spoke pretty loud and clear when they elected him president".
"It's been simmering on the stove with the lid on, like a pressure cooker", she said. Her cousin was a Republican governor.
"I do not recognize the man these ladies are describing", Ann Eubank, a fixture in Alabama Republican politics, said of the accusers. "He will not stop fighting for the people of Alabama", she said.