The federal prosecutors overseeing former President Donald J. Trump’s indictment on charges of seeking to overturn the 2020 election asked a judge on Friday night to impose a protective order over the discovery evidence in the case, citing a threatening message that Mr. Trump had posted on social media.

By mentioning the incendiary post in an otherwise routine request seeking to keep Mr. Trump from making evidence public, the prosecutors in the office of the special counsel, Jack Smith, were drawing the attention of the judge, Tanya S. Chutkan, to Mr. Trump’s longstanding habit of attacking those involved in criminal cases against him.

Hours later, Mr. Trump’s campaign responded with a statement calling the post “the definition of political speech.” The statement suggested that the post had not been directed at anyone involved in the election interference case, saying it was meant for Mr. Trump’s political adversaries.

The exchange of words began on Friday evening when Mr. Trump — with little warning or explanation — posted a message on Truth Social, his social media platform, that issued a vague but strongly worded threat.

“IF YOU GO AFTER ME, I’M COMING AFTER YOU!” he wrote.

Shortly after, in a standard move early in a criminal prosecution, the government filed its request for a protective order in the case to Judge Chutkan. Prosecutors noted that protections over discovery were “particularly important” in this instance given that Mr. Trump “has previously issued public statements on social media regarding witnesses, judges, attorneys and others associated with legal matters pending against him.”

To prove their point, they included a screenshot of the former president’s threatening post from that same evening.

A short time after the government’s filing, Mr. Trump’s campaign issued a statement with no aide’s name attached, insisting he was practicing his First Amendment rights.

“The Truth post cited is the definition of political speech,” the statement said, adding that it was in response to “dishonest special interest groups” and political committees attacking him.

That Mr. Trump is a political candidate exercising free speech is going to be an element of his defense in the latest case against him. Also Friday, Mr. Trump’s campaign posted on X, the site formerly known as Twitter, a 60-second ad describing the five prosecutors who have or are considering cases against him as the “fraud squad” acting on behalf of President Biden. (Those include the New York attorney general, Letitia James, who has brought a civil action.)

The ad represents one of Mr. Trump’s most aggressive denigrations of the prosecutors, whom he has consistently denounced. He has also promised that if elected, he would appoint a “real” special prosecutor to investigate Mr. Biden and his family, proposing eliminating the post-Watergate norm of Justice Department independence.

But the Truth Social post was more direct than comments he has made in the past, in a case where a key aspect of the indictment describes how Mr. Trump’s repeated and false public claims that he was a victim of widespread election fraud led to the violent attack by a pro-Trump mob at the Capitol on Jan. 6, 2021.

Judge Chutkan, who was randomly assigned the case when the indictment was filed on Tuesday, has not yet responded to the government’s request. But other judges in cases involving Mr. Trump have warned him about using threatening language.

At a court hearing in Manhattan in April, Justice Juan M. Merchan, who is overseeing Mr. Trump’s state prosecution on charges stemming from a hush payment to a porn actress, warned the former president to refrain from making comments that were “likely to incite violence or civil unrest.”

Justice Merchan’s admonition came after Mr. Trump posted on Truth Social saying that “death and destruction” could follow if he were charged in the case in Manhattan.

That same month, Judge Lewis A. Kaplan, who was presiding over a federal rape and defamation lawsuit filed against Mr. Trump by the writer E. Jean Carroll, warned the former president to stop posting messages about the case. The ones he had already written were “entirely inappropriate,” the judge said.

Mr. Trump had derided the case on social media as a “scam” and personally mocked Ms. Carroll.

Mr. Trump has often ignored such warnings and continued with impunity to post threatening or spiteful messages online.

After the hearing in front of Justice Merchan, Mr. Trump returned to Florida and to his customary practice, calling the district attorney who brought the New York charges against him, Alvin L. Bragg, a “criminal,” and Justice Merchan himself “a Trump-hating judge with a Trump-hating wife and family.”

Days after Judge Kaplan issued his warning, Mr. Trump attacked him too, saying on a trip to one of his golf courses in Ireland that the judge was “extremely hostile.”