Federal prosecutors on Sunday asked the judge handling former President Donald J. Trump’s trial on charges of plotting to overturn the 2020 election to reject his request to freeze the case in its entirety as Mr. Trump appeals her recent ruling that he is not immune from prosecution.

The prosecutors told the judge, Tanya S. Chutkan, that even as the former president’s appeal of the immunity decision moved forward, she should continue working on several of the unresolved legal issues in the case and not postpone the trial’s current start date of March 4.

“During the pendency of the appeal, any number of matters could arise in this case that are not involved in the appeal,” wrote Molly Gaston, a top deputy to Jack Smith, the special counsel who is overseeing Mr. Trump’s federal prosecutions. “The court should not enter an order preventing it from handling them.”

“For its part,” Ms. Gaston went on, “in light of the public’s strong interest in a prompt trial, the government will seek to ensure that trial proceeds as scheduled.”

The three-page filing by Ms. Gaston came just days after Mr. Trump’s lawyers asked Judge Chutkan to pause all of the dates and deadlines associated with the proceeding until the appeal of her decision denying their immunity claims is resolved.

The expansive stay Mr. Trump’s lawyers have asked for would in essence stop the case in its tracks. The appeal is the centerpiece of a long-planned strategy by the former president’s legal team to postpone the trial in Federal District Court in Washington until after the 2024 election.

This month, Judge Chutkan turned down Mr. Trump’s sweeping claims that he enjoyed “absolute immunity” from the election interference indictment because it was based on actions he took while he was in office.

In her ruling, she condemned his attempts to “usurp the reins of government” and said there was nothing in the law, the Constitution or American history upholding the idea that a former president should not be bound by the federal penal code.

Mr. Trump’s lawyers have already moved to challenge that decision in front of a federal appeals court in Washington and plan to keep appealing it all the way to the Supreme Court, if needed. But winning the argument is only one of their goals. They are also hoping to eat up time and postpone the case from going to trial for as long as they can.

If the trial were to be put off until after the election and Mr. Trump were to win, he could have his attorney general simply dismiss the charges. Holding a trial after the presidential race was over would also mean that voters would never get to hear any of the evidence that prosecutors have collected about Mr. Trump’s expansive efforts to reverse the results of the last election before weighing in on whether to elect him again in 2024.

Mr. Smith’s team has suggested in court papers that it knew Mr. Trump would seek to use the immunity appeal to delay the case. Last month, the prosecutors specifically asked Judge Chutkan to make her decision on the question quickly so that the appellate process could get underway.

But in her filing on Sunday evening, Ms. Gaston suggested there was no reason Judge Chutkan could not make rulings on other outstanding issues in the case as the appeal went forward. Among those issues is an unresolved motion by Mr. Trump’s lawyers to have the election charges dismissed because they represent what they have described as a partisan attack against him by President Biden.

While the defense and the prosecution have been sparring for months over the timing of the election interference trial, they have more recently been fighting over something else: a number of “speculative and conspiratorial” theories, as the government has called them, that Mr. Trump has indicated he may raise during the trial.

On Saturday night, in a separate set of court papers, prosecutors pushed back against those theories, which could serve as the basis for one of Mr. Trump’s lines of defense at trial: suggesting, that in reassuring the public that the 2020 election was conducted fairly, the so-called deep state was in fact misleading the nation, an assertion that lacks any credible basis.

In the papers filed on Saturday, Thomas P. Windom, another one of Mr. Smith’s top deputies, dismissed the notion — first brought up last month by Mr. Trump’s lawyers — that the SolarWinds computer hack engineered by Russia might have affected the results of the election.

Mr. Windom also rejected as “bewildering” Mr. Trump’s claim that a statement issued by the country’s top cybersecurity official saying that the 2020 election had been safe was “part of a partisan effort to provide false assurances to the public.”

Mr. Windom had little patience for yet another conspiratorial claim raised by Mr. Trump: that a cabal of politically motivated intelligence and national security officials had worked together after the election to convince him that no voting machines had been compromised and that the vote count had in fact been accurate.

Calling the idea “theatrical,” Mr. Windom said prosecutors never found a shred of evidence during their long investigation that “a domestic or foreign actor flipped a single vote in a voting machine.”

He also revealed how deeply the inquiry delved into the country’s national security community, noting that investigators interviewed the former director of national intelligence, the former national security adviser and his deputy, the former secretary of defense and the former leadership of the Justice Department. Asked if they were aware of any evidence of meddling in the election results, “the answer from every single official was no,” Mr. Windom’s filing said.