Leigh Corfman, now 53, told The Washington Post in an article published Thursday that Moore, then a 32-year-old assistant district attorney, took off her shirt and removed his clothes in the 1979 incident. He touched her over her bra and led the child's hands to touch him over his underwear, she said.
"I wanted it over with - I wanted out," Corfman told the paper. "Please just get this over with. Whatever this is, just get it over."
Three other women said Moore also made sexual advances to them when they were teenagers around the same time, according to the newspaper. Wendy Miller said she was working as a Santa's helper at a mall when she was 14 when Moore first approached her. By the time she was 16, Moore was allegedly asking her out on dates.
The age of consent was and continues to be 16 in Alabama.
Moore, in a written statement to the Post, denied doing anything inappropriate.
"These allegations are completely false and are a desperate political attack by the National Democrat Party and the Washington Post on this campaign," Moore said.
In the past, Moore has blasted same-sex marriage, referred to Islam as a "false religion," and said the Sept. 11 terror attacks were punishment for the United States' godlessness.
A special election for the U.S. Senate seat in Alabama vacated by now-Attorney General Jeff Sessions takes place Dec. 12. Moore is up against Democrat Doug Jones.