Supporters of Republican US presidential nominee Donald Trump recite the US Pledge of Allegiance at a campaign rally in Panama City, Florida, US, October 11, 2016. [Photo/Agencies]

That video has damaged Trump's poll numbers, particularly with women voters. He was chastised by Republican leaders, and some called on him to drop out of the presidential race.

Trump has apologized for his remarks, which he called private "locker room" talk. During the presidential debate on Sunday, he said he had not actually kissed women without permission nor groped them.

That assertion was what spurred one of the women to speak out, the New York Times said in its report.

"He was like an octopus," said Leeds, now 74. "His hands were everywhere."

The New York Times reported that Trump, in an angry phone call, denied the incidents and threatened to sue the newspaper.