Federal prosecutors tried for a second time on Friday to ask the judge overseeing former President Donald J. Trump’s classified documents case to bar him from making any statements that might endanger F.B.I. agents involved in the proceeding.

The move by the prosecutors came three days after the judge, Aileen M. Cannon, denied their initial request to keep Mr. Trump from attacking the agents on the procedural grounds that they had failed to properly inform Mr. Trump’s lawyers about their intentions.

The dispute, which has unfolded in back-and-forth filings in Federal District Court in Fort Pierce, Fla., began about 10 days ago when Mr. Trump falsely claimed on social media that the F.B.I. had authorized agents to kill him during their August 2022 search of Mar-a-Lago, his private club and residence in Florida, in which they discovered more than 100 classified documents.

Prosecutors have asserted that the former president’s remarks — including one in which he baselessly said agents were “locked & loaded ready to take me out” — were a “grossly misleading” misinterpretation of an F.B.I. operational plan for the search that was recently unsealed as part of a motion to suppress the fruits of the Mar-a-Lago search.

At the start of the Memorial Day weekend, the prosecutors asked Judge Cannon to revise Mr. Trump’s conditions of release to prohibit him from making any further public comments that might threaten or otherwise endanger the agents. It was the first time that prosecutors in the office of the special counsel, Jack Smith, had requested anything resembling a gag order in the case, although he has been under gag orders in two of his three other criminal proceedings.

On Tuesday, Judge Cannon denied the request, chiding members of Mr. Smith’s team for having ignored “professional courtesy” by failing to properly follow the “meet and confer” process for informing defense lawyers of the motion they planned to file. But she allowed prosecutors to resubmit their request after they met with Mr. Trump’s lawyers in a more expansive fashion and included a verbatim statement from them on how the process of meeting and conferring had gone.

The motion prosecutors filed on Friday was nearly identical to their initial submission. It included the statement from Mr. Trump’s lawyers that Judge Cannon had asked for, which asserted that Mr. Trump opposed any efforts to limit his public statements and requested that officials in the court’s pretrial services office, which oversees release conditions, give their views on “the significant and complex constitutional issues” the prosecutors had raised before the judge considered them.