At the federal courthouse in Washington, a woman called the chambers of the judge assigned to the election interference case against former President Donald J. Trump and said that if Mr. Trump were not re-elected next year, “we are coming to kill you.”

At the Federal Bureau of Investigation, agents have reported concerns about harassment and threats being directed at their families amid intensifying anger among Trump supporters about what they consider to be the weaponization of the Justice Department. “Their children didn’t sign up for this,” a senior F.B.I. supervisor recently testified to Congress.

And the top prosecutors on the four criminal cases against Mr. Trump — two brought by the Justice Department and one each in Georgia and New York — now require round-the-clock protection.

As the prosecutions of Mr. Trump have accelerated, so too have threats against law enforcement authorities, judges, elected officials and others. The threats, in turn, are prompting protective measures, a legal effort to curb his angry and sometimes incendiary public statements, and renewed concern about the potential for an election campaign in which Mr. Trump has promised “retribution” to produce violence.

Given the attack on the Capitol by Trump supporters on Jan. 6, 2021, scholars, security experts, law enforcement officials and others are increasingly warning about the potential for lone-wolf attacks or riots by angry or troubled Americans who have taken in the heated rhetoric.

In April, before federal prosecutors indicted Mr. Trump, one survey showed that 4.5 percent of American adults agreed with the idea that the use of force was “justified to restore Donald Trump to the presidency.” Just two months later, after the first federal indictment of Mr. Trump, that figure surged to 7 percent.

The indictments of Mr. Trump “are the most important current drivers of political violence we now have,” said the author of the study, Robert Pape, a political scientist who studies political violence at the University of Chicago.

Other studies have found that any effects from the indictments dissipated quickly, and that there is little evidence of any increase in the numbers of Americans supportive of a violent response. And the leaders of the far-right groups that helped spur the violence at the Capitol on Jan. 6 are now serving long prison terms.

But the threats have been steady and credible enough to prompt intense concern among law enforcement officials. Attorney General Merrick B. Garland addressed the climate in testimony to Congress on Wednesday, saying that while he recognized that the department’s work came with scrutiny, the demonization of career prosecutors and F.B.I. agents was menacing not only his employees but also the rule of law.

“Singling out individual career public servants who are just doing their jobs is dangerous — particularly at a time of increased threats to the safety of public servants and their families,” Mr. Garland said.

“We will not be intimidated,” he added. “We will do our jobs free from outside influence. And we will not back down from defending our democracy.”

Security details have been added for several high-profile law enforcement officials across the country, including career prosecutors running the day-to-day investigations.

The F.B.I., which has seen the number of threats against its personnel and facilities surge since its agents carried out the court-authorized search of Mar-a-Lago, Mr. Trump’s private club and residence in Florida, in August 2022, subsequently created a special unit to deal with the threats. A U.S. official said threats since then have risen more than 300 percent, in part because the identities of employees, and information about them, are being spread online.

“We’re seeing that all too often,” Christopher A. Wray, the bureau’s director, said in congressional testimony this summer.

The threats are sometimes too vague to rise to the level of pursuing a criminal investigation, and hate speech enjoys some First Amendment protections, often making prosecutions difficult. But the Justice Department has charged more than a half dozen people with making threats.

This has had its own consequences: In the past 13 months, F.B.I. agents confronting individuals suspected of making threats have shot and fatally wounded two people, including one in Utah who was armed and had threatened, before President Biden’s planned visit to the area, to kill him.

In a brief filed in Washington federal court this month, Jack Smith, the special counsel overseeing the Justice Department’s prosecutions of Mr. Trump, took the extraordinary step of requesting a gag order against Mr. Trump. He linked threats against prosecutors and the judge presiding in the case accusing Mr. Trump of conspiring to overturn the results of the 2020 election to the rhetoric Mr. Trump had used before Jan. 6.

“The defendant continues these attacks on individuals precisely because he knows that in doing so, he is able to roil the public and marshal and prompt his supporters,” the special counsel’s office said in a court filing.

Mr. Trump has denied promoting violence. He says that his comments are protected by the First Amendment right to free speech, and that the proposed gag order is part of a far-ranging Democratic effort to destroy him personally and politically.

“Joe Biden has weaponized his Justice Department to go after his main political opponent — President Trump,” said Steven Cheung, a spokesman for the former president.

But Mr. Trump’s language has often been, at a minimum, aggressive and confrontational toward his perceived foes, and sometimes has at least bordered on incitement.

On Friday, Mr. Trump baselessly suggested in a social media post that Gen. Mark A. Milley, the departing chairman of the Joint Chiefs of Staff, might have engaged in treason, “an act so egregious that, in times gone by, the penalty would have been DEATH.” (General Milley has been interviewed by the special counsel’s office.)

The day before the threatening call last month to Judge Tanya S. Chutkan’s chambers in Federal District Court in Washington, Mr. Trump posted on his social media site: “IF YOU GO AFTER ME, I’M COMING FOR YOU!” (A Texas woman was later charged with making the call.)

Mr. Smith — whom Mr. Trump has described as “a thug” and “deranged” — has been a particular target of violent threats, and his office is on pace to spend $8 million to $10 million on protective details for him, his family and senior staff members, according to officials.

Members of his plainclothes detail were conspicuously present as he entered an already locked-down Washington federal courtroom last month to witness Mr. Trump’s arraignment on the election interference charges — standing a few feet from the former president’s own contingent of Secret Service agents.

On Friday, a judge presiding over a case in Colorado about whether Mr. Trump can be disqualified from the ballot there for his role in promoting the Jan. 6 attack issued a protective order barring threats or intimidation of anyone connected to the case. The judge cited the types of potential dangers laid out by Mr. Smith in seeking the gag order on Mr. Trump in the federal election case.

There have been recent acts of political violence against Republicans, most notably the 2017 shooting of Representative Steve Scalise of Louisiana. Last year an armed man arrested outside the home of Justice Brett M. Kavanaugh said he had traveled from California to kill the conservative Supreme Court jurist.

But many scholars and experts who study political violence place the blame for the current atmosphere most squarely on Mr. Trump — abetted by the unwillingness of many Republican politicians to object to or tamp down the violent and apocalyptic language on social media and in the conservative media.

In one example of how Mr. Trump’s sway over his followers can have real-world effects, a man who had been charged with storming the Capitol on Jan. 6 was arrested in June looking for ways to get near former President Barack Obama’s Washington home. The man — who was armed with two guns and 400 rounds of ammunition and had a machete in the van he was living in — had hours earlier reposted on social media an item Mr. Trump had posted that same day, which claimed to show Mr. Obama’s home address.

In his first two years out of office, Mr. Trump’s public comments largely focused on slowly revising the history of what happened on Jan. 6, depicting it as mostly peaceful. At his rallies and in interviews, he has described the rioters who have been arrested as “great patriots,” said they should be released, dangled pardons for them and talked repeatedly about rooting out “fascists,” “Marxists” and “communists” from government.

Mr. Trump’s verbal attacks on law enforcement agencies intensified after the F.B.I.’s search of Mar-a-Lago, as they pursued the investigation that later led to his indictment on charges of mishandling classified documents and obstructing efforts to retrieve them. Some of his most aggressive comments were made as it became clear that the Manhattan district attorney, Alvin L. Bragg, was likely to indict him last spring in connection with hush money payments to a porn actress.

He posted a story from a conservative news site that featured a picture of Mr. Bragg with an image of Mr. Trump wielding a baseball bat right next to it.

In another post, Mr. Trump predicted that there would be “potential death and destruction” if he were charged by Mr. Bragg. The district attorney’s office found a threatening letter and white powder in its mailroom hours later. (The powder was later determined not to be dangerous.)

Professor Pape, of the University of Chicago, said that while the numbers of people who felt violence was justified to support Mr. Trump were concerning, he would rather focus on a different group identified in his survey: the 80 percent of American adults who said they supported a bipartisan effort to reduce the possibility of political violence.

“This indicates a vast, if untapped, potential to mobilize widespread opposition to political violence against democratic institutions,” he said, “and to unify Americans around the commitment to a peaceful democracy.”

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