“Hunter’s decision won’t stop Trump from spreading debunked conspiracy theories about the past,” said David Axelrod, President Barack Obama’s former chief strategist. “But it does give Joe Biden an answer he didn’t have about potential conflicts of interest moving forward.”

In a brief news conference here Sunday in which he repeatedly pounded the podium, Mr. Biden stressed that the decision to leave the Chinese company’s board had been his son’s alone and suggested he learned of the statement from Hunter Biden’s lawyers. He also took what seemed to be veiled swipes at some of Mr. Trump’s children, who have had their own overseas business dealings.

“The statement my son put out today, which I saw when he put it out — I was told it was going to be put out, I did not consult with him about what’s being put out — in fact represents the kind of man of integrity he is,” Mr. Biden said. “ And I can tell you now, if I am your president, next president, I’m going to build on the squeaky-clean transparent environment that we had in the Obama-Biden White House, and no one in my family or associated with me will be involved in any foreign operation whatsoever. Period, end of story.”

Minutes later, he appeared to jab more sharply at members of the Trump family, a message that Mr. Biden, a Senate traditionalist who reveres beltway customs and civility, does not typically emphasize.

“No one in my family will have an office in the White House, will sit in on meetings as if they’re a Cabinet member, will in fact have any business relationship with anyone that relates to a foreign corporation or a foreign country,” he said.