“I gave a hook to some very unethical people to act in illegal ways to try to do some harm to my father,” he said. “That’s where I made the mistake. So I take full responsibility for that. Did I do anything improper? No, not in any way. Not in any way whatsoever.”

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Many Democratic strategists and officials have warned that the scrutiny on the Biden family has become a significant distraction for the former vice president, and poses perhaps the greatest threat yet to a candidacy that until recent weeks was well ahead in the polls. That makes it all the more urgent for Mr. Biden to land the kind of consistently fluent, forceful debate performance that has so far eluded him at a moment when Senator Elizabeth Warren has now surpassed him in some polls, Democratic operatives and activists said.

“I’m never a distraction to my dad, but as it relates to actually going and being onstage with him — this is not a family business,” Hunter Biden said Tuesday in the ABC interview, which aired on “Good Morning America’’ and was also excerpted online by the network. “Everybody kind of thinks that somehow, whether it’s a compliment that we’re like the Kennedys or whether it’s a, you know, backhanded compliment like you’re the Trumps, my dad has a, a job, but that does not mean that I have had any plans to go do rallies and, you know and, you know, talk about Donald Trump’s kids and I never will, you know, that’s not what Bidens do.”

At a news conference on Sunday, however, his father did appear to take some oblique swipes at the ethical practices of members of the Trump family, some of whom who have conducted their own overseas business dealings. And Hunter Biden seemed to be dismissive of Donald Trump Jr., who along with his father and brother have been highly critical of the Bidens.

“Donald Prince Humperdinck, um, Trump, Jr., is not somebody I really care about,” he said, an apparent reference to a character in the movie “The Princess Bride.”

In the interview, Hunter Biden signaled that by backing away from foreign dealings, he hoped to eliminate the controversy as a campaign issue for his father.

“I’m taking it off the table,” he said. “I’m making that commitment. Let’s see if anybody else makes that commitment. But that’s the commitment that I’m making.”