"I moved on her and I failed. I'll admit it," Trump is heard saying. It was unclear when the events he was describing took place. The tape was recorded several months after he married his third wife, Melania.
"Whoa," another voice said.
"I did try and f--- her. She was married," Trump says.
Trump continues: "And I moved on her very heavily. In fact, I took her out furniture shopping. She wanted to get some furniture. I said, 'I'll show you where they have some nice furniture.'"
"I moved on her like a bi**h, but I couldn't get there. And she was married," Trump says. "Then all of a sudden I see her, she's now got the big phony tits and everything. She's totally changed her look."
At that point in the audio, Trump and Bush appear to notice Arianne Zucker, the actress who is waiting to escort them into the soap opera set.
"Your girl's hot as s---, in the purple," says Bush, who's now a co-host of NBC's Today show.
"Whoa!" Trump says. "Whoa!"
"I've gotta use some tic tacs, just in case I start kissing her," Trump says."You know I'm automatically attracted to beautiful -- I just start kissing them. It's like a magnet. Just kiss. I don't even wait."
"And when you're a star they let you do it," Trump says. "You can do anything."
"Whatever you want," says another voice, apparently Bush's.
"Grab them by the p---y," Trump says. "You can do anything."
A spokeswoman for NBC Universal, which produces and distributes "Access Hollywood," declined comment.
"This was locker room banter, a private conversation that took place many years ago. Bill Clinton has said far worse to me on the golf course - not even close," Trump said in a statement. "I apologise if anyone was offended."
The tape appears at a time when Trump, the Republican presidential nominee, has sought to make a campaign issue out of his opponent's marriage. Trump has criticized former President Bill Clinton for his past infidelity, and criticized opponent Hillary Clinton as her husband's "enabler."
"Hillary Clinton was married to the single greatest abuser of women in the history of politics," Trump told the New York Times in a recent interview. "Hillary was an enabler, and she attacked the women who Bill Clinton mistreated afterward. I think it's a serious problem for them, and it's something that I'm considering talking about more in the near future."
Trump carried on a very public affair with Marla Maples - his eventual second wife - while still married to first wife Ivana Trump.
Trump has been criticized in this campaign for derogatory and lewd comments about women, including some made on TV and live radio. In an interview Wednesday with KSNV-TV, a Las Vegas television station, Trump said that those comments were made for entertainment.
"A lot of that was done for the purpose of entertainment. There's nobody that has more respect for women than I do," he told the station.
"Are you trying to tone it down now?" asked the interviewer, Jim Snyder.
"It's not a question of trying, it's very easy," said Trump.
The tape obtained by The Post seems to have captured Trump in a private moment, with no audience beyond Bush and a few others on the bus. It appears to have been shot around September 16, 2005, which was the day press reports said Trump would tape his soap-opera cameo.
The video shows the bus carrying Trump and Bush turning down a street on the studio backlot. The two men cannot be seen.
"Oh, nice legs, huh?" Trump says.
"Oof, get out of the way, honey," Bush says, apparently referencing somebody else blocking the view of Zucker.
The two men then exit the bus, and greet Zucker.
"We're ready, let's go," Trump says, after the initial greetings. "Make me a soap star."
"How about a little hug for the Donald?" Bush says. "He just got off the bus."
"Would you like a little hug, darling?" Zucker says.
"Absolutely," Trump says. As they embrace, and air-kiss, Trump says, "Melania said this was okay."
The video then follows Trump, Bush and Zucker into the studio. Trump did appear on Days of Our Lives, in late October. In a tape of that cameo posted online, Zucker's character asks Trump - playing himself - for a job at his business, and tells him suggestively, "I think you'll find I'm a very willing employee. Working under you, I think, could be mutually beneficial."
Trump's character gives her the brushoff.
"That's an interesting proposition," Trump says onscreen. "I'll get back to you."
A publicist for Zucker did not immediately respond to questions on Friday afternoon.
In a 2005 interview on the TV show Soap Talk, posted online, host Lisa Rinna asked Zucker if Trump was cute.
"He is so cute and charming," Zucker said. "You just don't look above..." she said, and motioned to her hairline.
Rosalind S. Helderman and Sarah Parnass contributed to this report.