Special counsel Jack Smith and his team have requested a federal judge in Washington, D.C., impose a "narrowly tailored" order restricting former President Donald Trump from making public statements that they argue could "present a serious and substantial danger of prejudicing" his 2020 federal election interference case.

In an extraordinary filing, Smith's office accused Trump of engaging in a sweeping campaign of "disinformation" and harassment intended to intimidate witnesses, prosecutors and others involved in the prosecution he is facing.

"Like his previous public disinformation campaign regarding the 2020 presidential election, the defendant's recent extrajudicial statements are intended to undermine public confidence in an institution -- the judicial system -- and to undermine confidence in and intimidate individuals --the Court, the jury pool, witnesses, and prosecutors," the filing says.

Trump has pleaded not guilty to charges of undertaking a "criminal scheme" to overturn the results of the 2020 election by enlisting a slate of so-called "fake electors," using the Justice Department to conduct "sham election crime investigations," trying to enlist the vice president to "alter the election results," and promoting false claims of a stolen election as the Jan. 6 riot raged -- all in an effort to subvert democracy and remain in power.

Prosecutors say their proposed order to D.C. District Judge Tanya Chutkan would be "a narrow, well-defined restriction" that would prohibit Trump from making statements "regarding the identity, testimony, or credibility of prospective witnesses" and "statements about any party, witness, attorney, court personnel, or potential jurors that are disparaging and inflammatory, or intimidating."

The order would not prohibit Trump from quoting or referencing public court records or making proclamations of innocence, prosecutors say.

But if implemented by Judge Chutkan, such an order would likely set off a high-stakes legal battle, with Trump -- who is currently the frontrunner for the 2024 Republican presidential primary -- expected to argue that his First Amendment rights are being violated.

In their filing, the special counsel's office cites multiple public statements and Truth Social posts from Trump in the months since his indictment that they argue contain deliberate falsehoods intended by Trump to gin up the ire of his supporters.

"The defendant knows that when he publicly attacks individuals and institutions, he inspires others to perpetrate threats and harassment against his targets," they write. "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."

They specifically flag to Judge Chutkan attacks that Trump has leveled at her personally, including posts where he called her "a fraud dressed up as a judge" and "a radical Obama hack."

They also point to a case from shortly after Trump's indictment in Washington in which a Texas woman was arrested for calling Chutkan's chambers and making racist death threats after it was revealed that Chutkan was assigned to Trump's case. "Multiple" other threats have been directed at Smith's office as well, they say, including threats to a specific prosecutor on his team singled out by Trump in past Truth Social posts.

"Given the defendant's history ... and the nature of the threats to the Court and to the Government, it is clear that the threats are prompted by the defendant's repeated and relentless posts," the filing reads. "To the extent that the defendant's public posts reach the general public, they also reach the jury pool for this trial."

The filing also seeks to debunk a claim Trump made late last month that a prosecutor from Smith's team "met with high officials at the White House ... just prior" to the special counsel seeking Trump's indictment in the classified documents case in June.

"In fact, as the defendant well knows from the formal FBI FD-302 interview report and agent notes that he received in discovery on June 21, 2023, in the Southern District of Florida case, on March 31, 2023, the Special Counsel's Office prosecutor conducted a routine investigative interview of a career military official at that official's duty station -- the White House," they write. "The defendant's objective in spreading a knowing lie to the contrary -- including by re-posting others' Truth Social posts naming the prosecutor and repeating the lie -- is an attempt to prejudice the public and the [jury pool] in advance of trial."

Smith's attorneys also single out Trump's attacks on potential witnesses for their case, including former Attorney General William Barr and former Vice President Mike Pence, which they argue is "an effort to influence the public's and the jury pool's impressions of potential witnesses outside of the courtroom."

"The defendant's repeated, inflammatory public statements regarding the District of Columbia, the Court, prosecutors, and potential witnesses are substantially likely to materially prejudice the jury pool, create fear among potential jurors, and result in threats or harassment to individuals he singles out," they say. "Put simply, those involved in the criminal justice process who read and hear the defendant's disparaging and inflammatory messages (from court personnel, to prosecutors, to witnesses, to potential jurors) may reasonably fear that they could be the next targets of the defendant's attacks."

It's unclear when Judge Chutkan might rule on the government's motion.

Trump has denied all wrongdoing and denounced the election interference charges as "a persecution of a political opponent." A spokesperson for Trump did not immediately respond to a request for comment from ABC News.