President Trump has opened a new front in his campaign to intimidate political foes, threatening a prominent liberal think tank with a $5 billion defamation lawsuit over a report concluding that his deployment of the National Guard to cities across the country has had little effect on reducing violent crime.

The threats against the think tank, the Center for American Progress, were Mr. Trump’s latest effort to use the legal system to punish critics for voicing unflattering facts and opinions generally protected by the First Amendment. And while it is unclear how far any suit the president might ultimately file will get in court, it could force the organization to spend money fighting it off and make it even more of a target of his allies and supporters.

On Monday, one of Mr. Trump’s personal lawyers, Alejandro Brito, wrote a letter to the center warning that he would file the suit if the group did not fully retract the report, which was published on its website on July 13. The letter, viewed by The New York Times, was addressed to the group’s president and chief executive, Neera Tanden, a longtime Democratic official who served as a senior adviser to President Joseph R. Biden Jr., and to several of its board members.

Mr. Brito claimed that the report about the National Guard was full of malicious and false statements. He gave Ms. Tanden and members of her board until 5 p.m. on Friday to retract it and apologize to Mr. Trump.

Ms. Tanden pushed back, saying in a statement that the center would “neither cower nor bend in the face” of legal action. She also defended the report, asserting that while its findings might have been “inconvenient to the Trump administration,” they were “grounded in rigorous, evidence-based research and analysis.”

“This threatened lawsuit’s attack on facts and evidence is baseless,” she added. “A fundamental protection of the First Amendment is to allow for the publication of facts and analysis that is contrary to the arguments and claims of any administration. A lawsuit is a transparent attempt to silence us.”

Mr. Trump has often lashed out at scholars and commentators for reproaching or critiquing him in the news media. And since winning re-election, he has filed a flurry of lawsuits against news organizations like the BBC and The Times, claiming they defamed him. He has even filed suit against the Des Moines Register, arguing that a poll the paper published before the 2024 election indicating that he would lose the vote in Iowa amounted to consumer fraud and election interference.

(The Times has filed its own suits against the administration, including two seeking increased access for its reporters at the Pentagon.)

The president has repeatedly claimed that his administration is the most transparent in American history. But he and his aides have used lawsuits and executive actions to go after law firms, universities and television networks. They have also used criminal tactics such as search warrants and grand jury subpoenas in an effort to pry loose sensitive information from reporters.

Many of these efforts have faltered once they reached court and faced judicial scrutiny. Mr. Brito himself has filed multiple failed suits on behalf of Mr. Trump. Last month, a federal judge in Florida referred Mr. Brito for potential disciplinary proceedings after ruling that a suit he filed for the president against the Internal Revenue Service amounted to an improper exercise in self-dealing.

The Center for American Progress report accused Mr. Trump of seeking to take credit for a nationwide decline in violent crime that began before he returned to the White House. The report determined that there was “no evidence” that the National Guard deployments had affected the crime rate, adding that they were poised to cost taxpayers more than $1.7 billion if they continued through the end of 2026.

The report asserted that the “primary goal” of the deployments was “never to stop crime.” Instead, it said they amounted to “a dangerous power grab by the Trump administration.”

The team that put the report together used an analysis based on homicide, violent crime and gun victimization data in cities where the National Guard was deployed — Washington, Los Angeles and Memphis — over the period from January 2023 to this February.

“This approach was employed to identify any statistical changes in crime trends associated with the deployment of the National Guard in specific cities,” its authors wrote.

Mr. Trump referred to the report on social media last week after watching a television segment about the report, which he described as “another Radical Left SCAM.” In the post, he threatened to sue the center and several of its funders, including the liberal financier George Soros, who has long served as a boogeyman for the administration.

A week later, Mr. Brito’s letter arrived at the center, saying that the president would sue if Ms. Tanden and her colleagues did not retract the report, issue an apology and give Mr. Trump unspecified financial compensation.

The letter ended with an all-caps salutation: “PLEASE GOVERN YOURSELVES ACCORDINGLY.”

On Friday, a lawyer for the center fired back in a letter of his own, deriding Mr. Trump’s accusations that he had been defamed.

“This is utterly absurd,” the lawyer, Kevin H. Metz, wrote to Mr. Brito. “Truth is not and cannot be defamation.”

Mr. Metz went on to say that the center welcomed the opportunity to make its case in court and receive more information on the National Guard deployments through the process of discovery.

Other think tanks of various political stripes have rallied to the center’s side.

“Independent organizations across the ideological spectrum must be free to express their analysis and opinions, and to challenge those in power without fear of political retaliation or legal intimidation,” said Peter Goettler, the president and chief executive of the libertarian Cato Institute. “Disagreements on matters of policy should be settled through open inquiry, evidence, and debate — not threats designed to silence criticism.”