Former President Donald J. Trump’s lawyers on Monday assailed a request by federal prosecutors to limit what he could say about a new flare-up in a case accusing him of illegally retaining classified documents after leaving office.

In an angry court filing, the lawyers pushed back hard against the request by the office of the special counsel, Jack Smith, to revise Mr. Trump’s conditions of release by forbidding him to make any public comments that might endanger federal agents working on the prosecution.

On Friday evening, Mr. Smith’s team requested what amounted to a limited gag order on Mr. Trump, prompted by what it called “grossly misleading” social media posts the former president made last week falsely claiming that the F.B.I. had been authorized to kill him when agents searched Mar-a-Lago, his Florida club and residence, in August 2022.

The former president’s statements were based on a recently unsealed operational order for the search that contained boilerplate language spelling out that the use of deadly force could be used only in case of emergency, a standard provision applied to all searches conducted by the bureau.

In their motion to Judge Aileen M. Cannon in Federal District Court in Fort Pierce, Fla., Mr. Trump’s lawyers said that Mr. Smith’s request was “an extraordinary, unprecedented and unconstitutional censorship application” that “unjustly targets President Trump’s campaign speech while he is the leading candidate for the presidency.”

Mr. Trump’s legal team said that Mr. Smith’s request should be stricken from the docket and that he and his prosecutors should face contempt sanctions for filing it in the first place.