During last week’s state dinner at the White House, Hunter Biden seemed to be everywhere. Upbeat and gregarious, he worked the pavilion with grins and gusto, shaking hands and hugging other guests.

One guest who surely did not want to chitchat with him, though, was Merrick B. Garland, the attorney general whose Justice Department just two days earlier reached a plea agreement in which the president’s son will likely avoid prison time.

The presence of the younger Biden at such a high-profile event so soon after the plea deal proved to be the buzz of the evening. It was all the more attention-grabbing given the risk of an accidental encounter with the nation’s chief law enforcement officer, who would rather cut off a thumb than be caught looking chummy with the target of an investigation that he had guaranteed would be conducted by the book.

It did not go unnoticed either when, just days later, there was Hunter Biden getting on and off Marine One with the president heading to and from Camp David for the weekend.

In the nation’s capital, where such things are rarely accidental and always noticed, the oh-so-public appearances came across as an in-your-face message of defiance by a president determined to show that he stands by his son in the face of relentlessly toxic attacks. Yet some Democrats, including current and former Biden administration officials, privately saw it as an unnecessary poke-the-bear gesture.

“He knew exactly what he was doing, and he was willing to sustain the appearance issues to send a message to his son that he loves him,” said Norman Eisen, who was the ethics czar in President Barack Obama’s White House when Mr. Biden was vice president.

Had he been advising Mr. Biden, Mr. Eisen said, he would have warned him about “the flak they were going to take” but added that it would be a matter of optics, rather than rules. “That’s probably more of a question for an etiquette czar than an ethics czar,” he said. “Certainly, there’s no violation of any ethics rule as long as they didn’t talk about the case.”

The White House said Mr. Biden was simply being a father.

“In all administrations, regardless of party, it’s common for presidential family members to attend state dinners and to accompany presidents to Camp David,” Andrew Bates, a White House spokesman, said on Tuesday. “The president and first lady love and support their son.”

The visuals at the White House in the week since Hunter Biden’s plea deal was announced highlight the thorny situation for a president with a 53-year-old son traumatized by family tragedy and a devastating history of addiction to alcohol and crack cocaine. While Democrats scorn the conspiratorial fixation of the hard right on Hunter’s troubles, some of the president’s allies privately complain that, however understandably, he has a blind eye when it comes to his son. They lament that he did not step in more assertively to stop the younger man from trading on the family name in business dealings.

It is not a subject that advisers raise with Mr. Biden easily, if at all, and so many of them are left to watch how he handles it and react accordingly. They take solace in the belief that many Americans understand a father’s love for his son, even one who makes mistakes, and in the assumption that it will not significantly hurt Mr. Biden’s bid for re-election next year any more than it did his victory over President Donald J. Trump in 2020. And they recognize that no matter what the family does, Hunter will be a target for the next 16 months.

The plea deal last week was fraught for many reasons. It meant that the president’s son was admitting to criminal behavior by failing to file his taxes on time and would be subject to a diversion program on a felony charge of illegal gun possession, but would be spared time behind bars if a judge approves. Republicans immediately denounced it as a “sweetheart deal” by the Biden team.

In fact, the decision was announced by a Trump appointee, David C. Weiss, a U.S. attorney who was kept on by the Biden Justice Department so as not to appear to interfere in his inquiry into Hunter Biden. Mr. Garland and Mr. Weiss have both insisted that Mr. Weiss had what he called “ultimate authority” over the case.

There is no evidence that the president or the White House has played any role — unlike Mr. Trump, who while in office openly and repeatedly pressured the Justice Department to prosecute his perceived enemies and drop cases against his allies.

But congressional Republicans have been promoting two I.R.S. “whistle-blowers” who assert that the Justice Department restrained Mr. Weiss, despite his own denial. Republicans plan to call Mr. Weiss to testify in coming days and are threatening to impeach Mr. Garland.

One of the I.R.S. agents produced a message sent by Hunter Biden in 2017 invoking his father, who was then out of office, in pressuring a potential Chinese business partner to agree to a deal. While repeating that the president “was not in business with his son,” the White House has not disputed the authenticity of the message nor commented on the impression that Mr. Biden, as a former vice president, may have been used to secure business.

Asked by a reporter on Monday whether he had lied when he previously said he did not discuss Hunter’s business dealings with him, the president said simply, “No.”

Hunter Biden has appeared with his father since the start of his presidency, including previous trips to Camp David or the family home in Delaware. Hunter attended the first state dinner of the Biden presidency in December and accompanied his father on a trip to Ireland this spring.

So in that sense, it might not have been all that surprising that he showed up last Thursday for the state dinner for Prime Minister Narendra Modi of India. But it quickly set off Republicans and conservative media.

“Hunter and Merrick hanging out at Joe’s place?” Representative Andy Ogles, Republican of Tennessee, wrote on Twitter. “Classic Biden Crime Family.”

Representative Jason Smith, Republican of Missouri, said on Fox Business: “We saw a fancy state dinner at the White House, and you have the person who’s accused of these criminal allegations and also the department that has slow-walked these allegations, the leader of that department, seated and dining at the same table. All of this smells bad.”

The tuxedo-clad Hunter Biden appeared in high spirits at the dinner, making his way around the pavilion set up on the South Lawn. He put his arm around Bill Nelson, the NASA administrator and former senator from Florida, and gave a friendly shoulder grip to Andy Moffit, the husband of Gina Raimondo, the commerce secretary. Mr. Garland stayed resolutely on the other side of the pavilion, at least while reporters and photographers were there to watch.

While Mr. Garland was invited weeks beforehand, some who know him suspected he must not have known that Hunter Biden would be there and likely would have been upset to be put in such an awkward position. One person familiar with the dinner said those not on the White House staff were not given the guest list in advance. Representatives for the White House and Justice Department would not say whether the president’s staff gave the attorney general a heads up.

Still, even Democrats who would have preferred that Mr. Biden had not made such a public display of his son in the immediate aftermath of the plea deal bristle at criticism from Republicans who have shown little interest in nepotism involving Mr. Trump, who put his daughter and son-in-law on the White House staff and whose children have profited off his name for years.

David M. Axelrod, who was a senior adviser to Mr. Obama, said the state dinner made clear what Mr. Biden wanted to make clear — that he would not walk away from his son. “That may cause him problems, but it also reinforces a truth about a guy who has suffered great loss in his life and loves his kids,” he said.

Richard W. Painter, who was the chief White House ethics lawyer under President George W. Bush, later ran unsuccessfully for Congress as a Democrat and has been critical at times of ethical decisions by the Biden team, said the president is forced to balance his personal and campaign imperatives.

“These are the political calls that are made by the president,” said Mr. Painter, who according to media reports has been consulted by Hunter Biden’s lawyers about setting up a legal defense fund. “He wants to protect his political position running for re-election. He also wants to be a good father. That was his decision. You’re going to get heat. But I understand why he made the decision.”

Glenn Thrush contributed reporting.

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