For Billy Bush, the presidential cousin and genial Hollywood interviewer, 2016 was supposed to be a transformative year.
But not like this.
Just weeks after starting a prestigious gig as a host on NBC’s “Today” show, Mr. Bush on Friday found himself cast in a harsh and unflattering light — and facing scattered calls online to resign — after a recording emerged of him exchanging lewd and misogynistic remarks about women with Donald J. Trump.
In the recording, from 2005, Mr. Bush can be heard laughing as Mr. Trump describes in vulgar terms his efforts to seduce a married woman. The men, who were taping a segment for “Access Hollywood,” then boisterously admire the looks of a nearby television actress, with Mr. Bush shouting, “Yes, the Donald has scored!”
When Mr. Trump boasts that as a celebrity, he “can do anything” with women, another voice, apparently Mr. Bush’s, laughs and says, “Whatever you want.”
Mr. Bush, 44, issued a statement on Friday evening, writing: “Obviously I’m embarrassed and ashamed. It’s no excuse, but this happened 11 years ago — I was younger, less mature, and acted foolishly in playing along.”
A spokesman for NBC declined to comment. Network executives said they had no current plans to discipline Mr. Bush. But Mr. Bush’s position could become precarious if there is a strong and sustained backlash against the tape.
Already his Facebook page was being flooded with hundreds of outraged comments, many from women, a group that “Today” counts as a crucial part of its audience.
“Just saw the video with you and Donald Trump,” wrote a Facebook user named Gina Preziosi, beneath a picture of Mr. Bush handing out strips of bacon to a group of “Today” viewers. “You’re as scummy as he is.”
“WOW,” wrote a woman named Lavern Smith. “You’re such a pig.”
Mr. Bush’s move to the 9 a.m. slot of the “Today” show, announced in May, was viewed as a major career leap. But he struggled to adapt his preppy persona to the gauzier realm of morning television, and tensions with co-stars soon spilled into the open, including an on-air rebuke from Al Rokerwhen Mr. Bush defended the Olympic swimmer Ryan Lochte.
The recording of Mr. Bush with Mr. Trump, published on Friday afternoon by The Washington Post, was particularly ill-timed: The television industry is facing scrutiny over its treatment of women after a spate of sexual harassment allegations at Fox News.
Mr. Bush, a cousin of former President George W. Bush, is known as a gung-ho entertainment journalist with a talent for cozying up to celebrities, a skill he honed for 15 years on “Access Hollywood.”
“I bang around,” he told The New York Times in 2002. “Hanging around with people, that’s my thing.”
One of those people was Mr. Trump. On several occasions, Mr. Bush hosted the Miss Universe pageant, which was once owned by Mr. Trump, and in November 2004 he accompanied the real estate developer as he cast his presidential ballot.
“Billy has covered and interviewed literally everyone in Hollywood,” Noah Oppenheim, a senior “Today” show producer, wrote in a memo announcing his hiring this year.
But Mr. Bush’s go-along, get-along style proved a liability at this summer’s Olympics in Brazil. Mr. Bush had appeared to score a journalistic coup by interviewing Mr. Lochte shortly after the swimmer claimed to have been robbed at gunpoint.