The federal prosecutors overseeing the classified documents case against former President Donald J. Trump said in court papers on Friday that the evidence they are poised to give the defense as part of the normal process of discovery contained information about “ongoing investigations” that could “identify uncharged individuals.”

The court papers — a standard request to place a protective order on the discovery material — contained no explanation about what those other inquiries might be or whether were they related to the indictment detailing charges against Mr. Trump of illegally retaining dozens of national defense documents and obstructing the government’s efforts to get them back. The papers also did not identify who the uncharged people were.

Still, the reference to continuing investigations was the first overt suggestion — however vague — that other criminal cases could emerge from the work that the special counsel Jack Smith has done in bringing the Espionage Act and obstruction indictment against Mr. Trump in Miami last week.

Mr. Smith is also overseeing the parallel investigation into Mr. Trump’s efforts to reverse his election loss in 2020 and the ensuing assault on the Capitol by a mob of his supporters on Jan. 6, 2021.

Some witnesses close to Mr. Trump have been questioned by Mr. Smith’s team in connection with the both the documents and election interference inquiries.

The government’s motion for a protective order, which Mr. Trump’s lawyers did not oppose, said that prosecutors were ready to start turning over a trove of nonclassified evidence that they had collected during the documents investigation. That included information about investigative techniques, material related to potential witnesses and things like grand jury transcripts, exhibits and recordings of witness interviews, the motion said.

It also sought to restrict disclosure of the evidence to Mr. Trump’s legal team; to people who might be interviewed as witnesses and their lawyers; and to any others who were specifically authorized by the court.

At some point, Mr. Smith’s team will have work out a process for sharing with Mr. Trump’s lawyers the 31 highly sensitive documents at the center of the prosecution, some of which concern nuclear and military capabilities. On Thursday, Judge Aileen M. Cannon, a Trump appointee who is presiding over the case, told the lawyers that they needed to begin the process of obtaining security clearances to review the classified documents.

On Friday, two of Mr. Trump’s lawyers — Todd Blanche and Christopher M. Kise — notified Judge Cannon that they had reached out to the Justice Department to expedite the process of getting a clearance, which could take about a month.

Shortly after the government requested the protective order, Judge Cannon asked the federal magistrate judge assigned to help her with the case, Bruce E. Reinhart, to handle the question of whether to impose it. It is common in the Southern District of Florida for magistrate judges, not district judges like Judge Cannon, to handle pretrial motions.

Judge Reinhart is no stranger to the case. Last summer, he issued a warrant used by the F.B.I. to search Mar-a-Lago, Mr. Trump’s private club and residence in Florida, suggesting that he believed there was probable cause that investigators would find evidence of a crime at the compound.

It could be a significant development moving forward if Judge Reinhart handles the more substantial legal motions that will be filed by Mr. Trump’s lawyers in the months to come, given that Judge Cannon was widely criticized for make rulings favorable to Mr. Trump in an early stage of the investigation.

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