LONDON — The video, dark and grainy, shows a man identified as Prince Andrew of Britain standing in a doorway and waving goodbye to a young woman, then giving a look around before quickly shutting the door.

The footage was published on Sunday by The Daily Mail, a British tabloid, which says it was taken in December 2010 at a mansion in New York City owned by Jeffrey Epstein, the convicted pedophile who hanged himself in his jail cell this month. At the time, Mr. Epstein was a registered sex offender.

Buckingham Palace issued a statement Monday saying that the prince was “appalled” by the allegations against Mr. Epstein and rejecting any suggestion that the prince would take part in the “exploitation of any human being.” The statement did not challenge the authenticity of the video.

“His Royal Highness deplores the exploitation of any human being and the suggestion he would condone, participate in or encourage any such behavior is abhorrent,” the statement said.