Federal prosecutors on Monday asked a judge to reject a barrage of motions filed last month by former President Donald J. Trump that sought to toss out the indictment charging him with plotting to overturn the 2020 election and said his claims were full of “distortions and misrepresentations.”

In a 79-page court filing, prosecutors in the office of the special counsel, Jack Smith, went one by one through Mr. Trump’s multiple motions to dismiss the case and accused him and his lawyers of essentially trying to flip the script of the four-count indictment filed against him in August.

“The defendant attempts to rewrite the indictment, claiming that it charges him with wholly innocuous, perhaps even admirable conduct, — sharing his opinions about election fraud and seeking election integrity,” James I. Pearce, one of the prosecutors, wrote, “when in fact it clearly describes the defendant’s fraudulent use of knowingly false statements as weapons in furtherance of his criminal plans.”

When Mr. Trump first filed his motions to dismiss the case, they represented a breathtaking effort to reframe the various steps he took to remain in power after losing the election as something other than crimes.

For example, Mr. Trump sought to portray his repeated efforts to use false claims that the election had been stolen as “core political speech” protected by the First Amendment. He similarly tried to recast his lies about the election as “opinions” that he tried to use to build support for his wide-ranging efforts to overturn the results of the race.

But Mr. Pearce shot back on Monday for the Justice Department, saying that the First Amendment did not protect “criminal conduct” like using lies in a plot to defeat the will of the voters. He also wrote that Mr. Trump’s efforts to recast the meaning of the special counsel’s indictment in his own favor were “based on an inaccurate and self-serving characterization of the charges.”

In a separate motion, Thomas P. Windom, another prosecutor on the case, rejected Mr. Trump’s arguments that the charges should be dismissed because they are part of a “selective and vindictive prosecution.”

As part of their flurry of filings last month, Mr. Trump’s lawyers sought to paint the election interference case as “a retaliatory response” by President Biden to go after Mr. Trump, the front-runner for the Republican Party’s 2024 presidential nomination.

The lawyers made those accusations even though the indictment had been brought by Mr. Smith, an independent special counsel, and after an extensive grand jury investigation.

Mr. Windom responded to the claims by noting they were “spurious” and “contrived from two newspaper articles citing anonymous sources.” Appearing to get his back up, he also mounted an angry defense of his colleagues on Mr. Smith’s team.

“The special counsel and career prosecutors in the special counsel’s office collectively have served in the Department of Justice for decades,” Mr. Windom wrote. “They have sworn oaths to support and defend the Constitution, and they have faithfully executed their prosecutorial duties in this case.”

As part of his selective prosecution claims, Mr. Trump had argued that even though he was not the first candidate in U.S. history to have created alternate slates of electors to the Electoral College in an effort to win an election, he was the only one to have suffered criminal charges for having done so.

Mr. Windom acknowledged that alternate slates had indeed been sparingly used going back to the time of Thomas Jefferson. But he maintained that “none of the historical examples the defendant points to involved deceitful and corrupt efforts” to “block the certification of the legitimate results of a presidential election.”

In yet a third filing, prosecutors rebuffed Mr. Trump’s attempt to strike from the indictment any mention of the violence that erupted at the Capitol on Jan. 6, 2021. As part of their motions to dismiss, his lawyers had asked Judge Tanya S. Chutkan to remove all references to the Capitol attack from the case given that none of the charges explicitly accuses Mr. Trump of inciting the mob of his supporters that stormed the building.

But writing for the government, Molly Gaston, a prosecutor in Mr. Smith’s office, asserted that Mr. Trump was “responsible for the events at the Capitol on Jan. 6” despite the lack of an incitement charge and that evidence about the attack was instrumental to the government’s case.

“That day was the culmination of the defendant’s criminal conspiracies to overturn the legitimate results of the presidential election,” Ms. Gaston wrote.

The series of filings on Monday was the second time Mr. Smith’s office has rebutted Mr. Trump’s attempts to have the election case thrown out before it goes to trial. Last month, they assailed his initial motion to dismiss, rejecting sweeping claims that he enjoys “absolute immunity” from prosecution because the indictment arose from actions he took while in the White House.

Last week, Mr. Trump’s lawyers asked Judge Chutkan to put the case on hold entirely as she considered the immunity claims — another example of the former president’s long-running efforts to delay the proceeding for as long as possible.

On Monday, Ms. Gaston asked Judge Chutkan to deny the request to pause the case.

“The defendant has an established record of attempting to disrupt and delay the court’s carefully considered trial date and pretrial schedule,” she wrote. “Now the defendant has timed his motion to stay these proceedings for maximum disruptive effect.”

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