Beverly Young Nelson said she was 16 and Moore a prosecuting attorney in his 30s when he groped her and tried to pull off her shirt and shove her head in his lap.
Moore then warned "no one will believe you" if she talked of it.
"I was twisting and struggling and begging him to stop," said Nelson, then a waitress at an Alabama restaurant.
Moore, 70, a Christian conservative, has refused to quit the election. And he said Nelson's accusations were "absolutely false."
The Washington Post first reported claims by four women about Moore assaults when they were teenagers. McConnell revealed that party officials were considering whether a Republican write-in candidate could be found to challenge Moore in the December 12 special election. He also said: "I believe the women."
Losing the seat could open the door for Democrats to cut into the Republicans' two-seat Senate majority.