Lawyers for former President Donald Trump asked a federal judge to allow an independent attorney to review all of the documents seized by the FBI during its search of Mar-a-Lago, including those labeled classified, because they didn’t trust the Justice Department to accurately represent what was in them.

“The government has not demonstrated that these records should remain classified.” That issue will be decided later,” Mr. Trump’s attorneys wrote in a Monday morning filing to the U.S. District Judge Aileen Cannon, who ordered the appointment of a special master in the case last week.

They disputed the status of approximately 100 classified documents that the Justice Department had indicated were central to a criminal investigation, providing their most specific arguments yet to counter prosecutors’ request to continue evaluating the documents for national-security concerns.

Mr. Trump’s brief on Monday is the latest in a flurry of court filings in what has become a procedurally complicated dispute, with judges overseeing the case facing threats.

After leaving menacing messages in Judge Cannon’s chamber, a Houston woman was arrested on federal charges of threatening a federal official and communicating across state lines with a threat to injure. Other threats were made against Judge Bruce Reinhart, a magistrate judge who had approved the warrant for the Aug. 8 search of Mar-a-Lago.

Tiffani Shea Gish, the woman, said she was “in charge of nuclear for the United States Government,” that Mr. Trump was “disqualified,” and that he was “marked for assassination.” “I’m also Trump’s hitman, so consider it a bullet to your head from Donald Trump himself,” the woman said, according to an FBI complaint, threatening to shoot Judge Cannon in front of her children in another message.

On Aug. 22, Mr. Trump’s lawyers asked the court to appoint a special master to review the documents seized at Mar-a-Lago last month and filter out any privileged materials.

Mr. Trump’s request was granted on September 5 by U.S. District Judge Aileen Cannon in South Florida. She halted the Justice Department’s investigation into the former president’s handling of presidential records, including all classified material, in her order, until the special master reviewed the thousands of pages of documents taken from the former president’s residence and private club.

Three days later, the Justice Department attempted to restart its investigation into any national-security risks posed by the classified documents, with the assistance of intelligence personnel, asking Judge Cannon to stay part of her ruling.

Prosecutors asked the judge for permission to resume their review of the 100 classified documents at the heart of the investigation, claiming that a special master was unnecessary. The documents are government property, according to the Justice Department, so Mr. Trump cannot demand that they be returned to him.

The Justice Department has also stated that it will challenge Judge Cannon’s appointment as special master. According to legal experts, prosecutors may not file an appeal if Judge Cannon grants their request for emergency relief.

On Friday, Mr. Trump’s attorneys indicated that they would oppose the government’s request for access to the limited set of documents. The former president’s team addressed the Justice Department’s request for interim relief in greater detail in Monday’s brief.

The Justice Department proposed two candidates for the role in a joint filing on Friday, while Mr. Trump’s lawyers proposed two others.

Mr. Trump’s team suggested Raymond J. Dearie, a former Chief Judge of the United States. District Court for the Eastern District of New York, who also served on the Foreign Intelligence Surveillance Court, and Paul Huck Jr., a former Jones Day partner who established his own firm and served as general counsel to former Florida Gov. Charlie Crist.

Barbara S. Jones, a retired federal judge from the United States, was proposed by the government. Southern District of New York District Court. She served as the special master who sorted through the materials seized by the government from Mr. Trump’s former personal attorney Michael Cohen, and later reprised that role after then-Trump lawyer Rudy Giuliani’s office and home were raided.