8 October 2016 Last updated at 08:02 BST
Mr Trump was responding to a released videotape in which he said "you can do anything" to women "when you're a star" and bragged about trying to grope and kiss women.
"I've never said I'm a perfect person nor pretended to be someone that I'm not," Mr Trump said.
"Anyone who knows me knows these words don't reflect who I am. I said it, I was wrong and I apologise."
Donald Trump has issued a televised apology after obscene comments made by the US presidential candidate in 2005 were made public.