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Rudolph W. Giuliani, Donald Trump, and Bill Clinton attend the 2008 Joe Torre Safe at Home Foundation Golf Classic at Trump National Golf Club on July 14, 2008 in Briarcliff Manor, New York.
In the recording from 2005, Trump boasted to television personality Billy Bush about being able to "grab" women "by the p----" because "when you're a star they let you do it." The recording was picked up by a hot mic.
"This was locker room banter, a private conversation that took place many years ago," Trump said in the statement. "Bill Clinton has said far worse to me on the golf course - not even close. I apologize if anyone was offended."
Trump, the Republican nominee for president, has often used former President Bill Clinton's past with women to attack Hillary Clinton, Trump's Democratic rival.
The tape was recorded several months after Trump married his third wife, Melania. Trump and Bush were aboard a bus and were arriving on the set of "Days of Our Lives" to tape a segment for Trump's upcoming cameo on the soap opera.
The tape began with Trump discussing a failed attempt to seduce a woman.
"I did try and f--- her," Trump said. "She was married. ... And I moved on her very heavily."
He also talked about how his fame helped him pick up women.
"When you're a star they let you do it," Trump said. "You can do anything. ... Grab them by the p----. You can do anything."
Allan Smith contributed to this report.