Vice President JD Vance made an unannounced visit to the Supreme Court last week to attend a private dinner in a wood-paneled conference room with Chief Justice John G. Roberts Jr. and dozens of the chief justice’s former law clerks.

Accompanying his wife, Usha, who clerked for the chief justice nearly a decade ago, Mr. Vance was making a social call, people familiar with the dinner said. But Mr. Vance’s friendly pop-by illustrated the awkward dance that has been underway between the Trump administration and the nation’s highest court, as the administration has at times appeared to woo the justices even as President Trump has repeatedly bullied and insulted them.

With the court preparing to issue major rulings in the coming weeks that will determine the fate of key aspects of the president’s agenda, Mr. Trump has vacillated between combative and conciliatory in his treatment of the justices.

He has seemed ever aware and at times resentful of the critical role the justices play in determining the lawfulness of his policies, with the court representing perhaps the one force in American government truly able to thwart his agenda. At the heart of the tension: a president who appears to believe that justices, especially those he appointed, should be loyalists rather than independent actors in a separate, equal branch of government.

Abigail Jackson, a White House spokeswoman, said in a statement that the American people have “always valued President Trump’s ability to freely speak his mind and share his thoughts directly with them” — including about the court.

The chief justice did not respond to a request for comment. A spokeswoman for Mr. Vance declined to comment.

Mr. Trump was furious with the court after it invalidated his sweeping tariffs in February. He called a news conference to vent, criticizing individual justices as “fools and lap dogs” and saying his two nominees who voted against him were “an embarrassment to their families.”

While past presidents have voiced disagreement and frustration with Supreme Court rulings, that kind of language and personal animosity has been unheard-of from a president.

Standing silently by his side was the solicitor general, D. John Sauer. Mr. Trump’s former personal lawyer represents the administration at the Supreme Court in a role that has traditionally been so trusted by the court that it is nicknamed the “10th justice.”

Despite Mr. Trump’s anger, the administration has abided by the court’s ruling in the tariffs decision. The U.S. government this month started to refund some of the roughly $160 billion collected from those tariffs, plus interest.

Days after the news conference, Mr. Trump toned things down at his State of the Union address, when he could have blasted the chief justice and other members of the court to their faces as they sat in their robes in the front of the House chamber. Instead, in his remarks, Mr. Trump merely declared the ruling to be “very disappointing.” Otherwise, he was cordial to the four justices who attended, shaking their hands and exchanging pleasantries as he made his way to the rostrum.

But in recent weeks, the president has returned to hammering the court, including in repeated social media posts, as he has been appearing to brace for another major loss when the court rules on his effort to end the guarantee of birthright citizenship. The decision is expected by late June or early July.

“It would be a disgrace if the Supreme Court of the United States allows that to happen,” Mr. Trump said during an event in the Oval Office on Thursday. “It’s all up to a couple of people, and I hope they do what’s right.”

Mr. Trump turned up the pressure in early April when he became the first sitting president to attend an oral argument at the court for the birthright citizenship case. He spent about an hour listening to the arguments before abruptly getting up and walking out while the session was still underway. Critics said it was a show of power designed to intimidate the justices.

The president subsequently complained in a social media post that the Supreme Court had “not even recognized or acknowledged” his presence.

At the same time, the president hosted all six of the justices nominated by Republican presidents to the White House last month for a state dinner honoring King Charles III of Britain and Queen Camilla. The dinner was held the night before the court heard a case about Mr. Trump’s immigration policies.

None of the three liberal justices attended, and neither the White House nor the court has said whether they were invited.

On Friday, two justices whom the president has praised were in the East Room of the White House. Justice Clarence Thomas swore in Kevin Warsh as the next chairman of the Federal Reserve. Justice Brett M. Kavanaugh also attended.

Three of the justices who took part in the state dinner — Neil M. Gorsuch, Amy Coney Barrett and Justice Kavanaugh — were picked by Mr. Trump during his first term, drawing them Mr. Trump’s particular attention and, at times, his ire. In a recent post, as he criticized Justices Gorsuch and Barrett for voting against his tariffs, he insisted they should have been “loyal to the person that appointed them.”

The justices seem to have struggled with whether or how forcefully to respond. They have not specifically addressed Mr. Trump’s personal insults and have not responded to requests for comment about his statements when asked. But they have at times politely pushed back in public appearances.

In recent interviews to promote his new children’s book, Justice Gorsuch has rejected assertions that the justices should be loyal to the president.

“My loyalty is to the Constitution, the laws of the United States,” he said in an interview with CBS News. “That’s the oath I took. It’s really just that simple.”

The chief justice too has gently denounced the personal attacks — but indirectly. During an appearance at Rice University in March, he said harsh rhetoric aimed at justices is “dangerous.”

“It’s got to stop,” he added, without specifying whose rhetoric he was describing or naming Mr. Trump.

In an interview with a federal judge last year, the chief justice defended the independence of the judiciary, saying its role is “to obviously decide cases but in the course of that to check the excesses of Congress or the executive.”

Colleen Sinzdak, a former law clerk to Chief Justice Roberts who argues frequently in front of the court, said the justices seem to be trying to stay above the political fray. By ignoring some of the attacks, the justices send the message that they see themselves as part of an institution rather than political actors scrumming with elected officials.

“It’s not supposed to be about you personally,” she said. “They are trying to embody that in how they are going about their business, and to the extent possible to do the things they would normally do — like going to state dinners.”

Likewise, Richard Lazarus, a law professor at Harvard who has written frequently about the court, said the justices appeared to be trying to treat Mr. Trump like any other party in a case when they seated him in the public gallery for the arguments in the birthright citizenship case, rather than in a special seat reserved for presidents that is used for courtroom ceremonies.

Still, he said the president’s personal attacks on individual justices were “out of bounds,” representing a unique assault that went beyond the traditional push and pull between the branches of government.

“It does damage to the court as an institution,” he said, and it “generates threats to the individual justices and their families when the president attacks them in this way.”

Professor Lazarus said he believed the justices should have declined to attend Mr. Trump’s state dinner last month, given that it appears only those nominated by Republican presidents had been invited.

“It’s wrong, irresponsible and undermines the integrity of the court, which all the justices tell us they believe in,” he said.

Ms. Jackson, the White House spokeswoman, said the president understands the dangers of political violence after three assassination attempts in less than two years.

“Any implication that sharing these opinions is akin to making threats is deeply unserious and should be dismissed by anyone with half a brain,” she said in a statement, adding that the administration “cares deeply for the safety of all members of the Judicial Branch.”

For his part, Mr. Vance, a graduate of Yale Law School, has not been shy about expressing his frustration with the courts and his wife’s former boss. In an interview with New York Times opinion columnist Ross Douthat last year, Mr. Vance said the chief justice was “profoundly wrong” to suggest that one of the roles for the court is to check the excesses of the executive branch. Courts, he said, should be “extremely deferential” to the president’s political judgments.

At the court last Saturday night, around 100 guests gathered for the reunion of law clerks, starting with cocktails in a courtyard, followed by dinner in one of the formal conference rooms on the same floor as the courtroom.

Mr. Vance and his wife were not given special seating at the chief justice’s table, said people familiar with the event who were granted anonymity to talk about the private dinner. And when Chief Justice Roberts gave brief remarks to welcome guests, he did not offer any special greeting to Mr. Vance.

For the night, the vice president was just a plus one.

Zolan Kanno-Youngs and Tyler Pager contributed reporting to this story.