The federal prosecutors overseeing the classified documents case against former President Donald J. Trump objected on Monday to his proposal to discuss highly sensitive discovery evidence at a secure location at Mar-a-Lago, his private club and residence in Florida.

Last week, Mr. Trump’s lawyers asked Judge Aileen M. Cannon, who is presiding over the case, to let the former president discuss the classified discovery evidence in the “secure facility” that he once used for such materials when he was in office. That facility, the lawyers said, was “at or near his residence,” an apparent reference to Mar-a-Lago, which is in West Palm Beach.

But in their own filing to Judge Cannon, prosecutors in the office of the special counsel, Jack Smith, said that Mr. Trump was seeking “special treatment that no other criminal defendant would receive” by requesting to discuss the classified material at home.

“In essence,” one of the prosecutors, Jay I. Bratt, wrote, “he is asking to be the only defendant ever in a case involving classified information (at least to the government’s knowledge) who would be able to discuss classified information in a private residence.”

Mar-a-Lago, Mr. Bratt went on, was especially unsuited to house discussions about classified material given that it is a social club with “more than 25 guest rooms, two ballrooms, a spa, a gift store, exercise facilities, office space, and an outdoor pool and patio.”

Moreover, Mr. Bratt wrote, “the Mar-a-Lago club had hundreds of members and was staffed by more than 150 full-time, part-time and temporary employees” who, from January 2021 to August 2022, worked at or attended “more than 50 social events, including weddings, movie premieres and fund-raisers that together drew tens of thousands of guests.”

Prosecutors want Judge Cannon to force Mr. Trump to discuss and review the classified discovery evidence in one of the SCIFs — or secure compartmented information facilities — run by the federal courts in Florida.

The dueling arguments over using Mr. Trump’s secure facility at Mar-a-Lago stem from the government’s attempts to put a protective order in place governing the handling of a trove of classified discovery materials that prosecutors are legally bound to turn over to Mr. Trump’s lawyers as part of the prosecution.

Those materials, the prosecutors noted in their filing to Judge Cannon, include far more than the 32 sensitive national security documents that Mr. Trump has been charged with taking with him after he left office. They also include what the government described as classified emails “about highly classified briefings given to then-President Trump” and “classified witness statements about then-President Trump’s knowledge about classified information.”

In their filing, prosecutors also reasserted their belief that one of Mr. Trump’s co-defendants in the case, Walt Nauta, his personal aide, should have only limited access to the classified discovery materials. That is despite Mr. Nauta also being charged with the former president and a third defendant — Carlos De Oliveira, the property manager at Mar-a-Lago — with conspiring to obstruct the government’s repeated efforts to retrieve the documents from Mr. Trump.

The prosecutors want Judge Cannon to impose a restriction that only Mr. Nauta’s lawyers can have free rein over the classified discovery, but can ask on a case-by-case basis to show it to him. They argued that Mr. Nauta should not be permitted to look at the materials without limitations because he no longer has a security clearance and has “not established that he has a need to know the sensitive information in the classified documents.”

The prosecutors are likely to request similar restrictions for Mr. De Oliveira.

This latest round of arguments about the protective order in the classified documents case came just days after the judge in the other federal case that Mr. Trump is facing — the one accusing him of conspiring to overturn the 2020 election — also imposed a protective order over the handling of discovery materials.

In that case, the judge, Tanya S. Chutkan, barred Mr. Trump and his lawyers from sharing or publicly commenting on any evidence, like witness interviews or grand jury testimony, that was designated as sensitive. Judge Chutkan also cautioned Mr. Trump against making any “inflammatory statements” about the case that might be construed as an attempt to intimidate witnesses or taint potential jurors.