The federal prosecutors who charged former President Donald J. Trump with conspiring to overturn the 2020 election pushed back on Thursday against one of his central defenses, rejecting his claims that he enjoyed “absolute immunity” from criminal prosecution because his indictment arose from actions he took while in the White House.

The prosecutors in the office of the special counsel, Jack Smith, said Mr. Trump’s expansive bid to claim immunity was unsupported by “the Constitution’s text and structure, history and tradition, or Supreme Court precedent.”

“The defendant is not above the law,” they wrote in a 54-page filing. “He is subject to the federal criminal laws like more than 330 million other Americans, including members of Congress, federal judges, and everyday citizens.”

The court papers, filed in Federal District Court in Washington, were a blunt rebuttal of Mr. Trump’s attempt to have Judge Tanya S. Chutkan, who is overseeing the case, dismiss the four counts he is facing before they go to trial. Though filled with technical jargon and arcane citations of the Federalist Papers, the government’s response to Mr. Trump boiled down to a simple argument: In the United States, the law equally applies to everyone.

Mr. Trump’s lawyers raised the immunity defense two weeks ago in a sweeping 52-page motion to Judge Chutkan. The motion, among other things, was an audacious effort to reframe the core of Mr. Smith’s indictment by arguing that all the counts accusing Mr. Trump of trying to subvert democracy and remain in power despite the will of the voters were, in fact, attempts to uphold his presidential duty to “ensure election integrity.”

The immunity motion marked the first — but surely not the last — attempt by Mr. Trump’s legal team to have the conspiracy charges tossed out before his trial begins in March. Those charges accuse him of defrauding the United States, obstructing the certification of the election and depriving people of the right to have their votes counted.

In the government’s new filing, James I. Pearce, a prosecutor, scoffed not only at the notion that a former president could be immune from prosecution, but also at Mr. Trump’s attempts to recast the charges contained in the indictment as efforts to uphold the law.

Mr. Pearce rejected the claim that Mr. Trump was acting within the scope of his “official duties” when he tried to enlist the Justice Department in validating his claims of election fraud or pressured state lawmakers to draft false slates of electors saying he had won states he actually had lost.

Those moves and others, Mr. Pearce said, were not related to Mr. Trump’s role as president, but rather to his partisan position as a politician seeking re-election.

“The allegations focus principally on the defendant’s actions as a candidate for elective office,” Mr. Pearce wrote. “Furthermore, the indictment alleges that the defendant acted deceitfully or corruptly to secure a personal benefit to himself as a presidential candidate, not to carry out constitutional obligations entrusted to the presidency.”

The Justice Department has long maintained a policy that sitting presidents cannot be indicted. But Mr. Trump’s immunity claims sought something broader: complete protection from criminal prosecution for any actions he took while he was in the White House, even though he no longer holds public office.

His lawyers were attracted to the argument in part because it has never been tested in the context of a criminal case.

In 1982, the Supreme Court ruled by a 5-to-4 margin that former President Richard M. Nixon was absolutely immune from a civil lawsuit arising from his official actions. But while John F. Lauro, the lawyer who wrote Mr. Trump’s initial brief, cited that case, Nixon v. Fitzgerald, extensively in his filing, the reasoning in its majority opinion did not address whether presidential actions could be prosecuted as crimes.

The claims of executive immunity also offered Mr. Trump’s legal team another advantage: They can be immediately challenged in appellate courts, including up to the Supreme Court. While those appeals could eat up time, in keeping with Mr. Trump’s longstanding strategy of trying to delay the case until after the 2024 election, legal experts have said the Supreme Court was unlikely to look favorably on the arguments.

Mr. Trump’s lawyers have suggested they might file a handful of other motions attacking the charges in the case, including attempts to challenge each of the three conspiracy counts he faces.

On Friday, they are scheduled to file papers related to a defense that they might raise during the trial — the so-called advice of counsel defense. That strategy would involve Mr. Trump blaming the stable of lawyers advising him after the election for giving him poor legal advice.