US prosecutors unsealed a 37-count indictment against Donald Trump on Friday, accusing the former president of risking some of the country's most sensitive security secrets after leaving the White House in 2021.

Trump mishandled classified documents that included information about the secretive US nuclear programme and potential domestic vulnerabilities in the event of an attack, the federal indictment said.

Trump also discussed with his lawyers the possibility of lying to government officials seeking to recover the documents; stored some documents in boxes around a toilet, and moved others around his Mar-a-Lago resort home in Florida to prevent them from being found, the charges said.

"Wouldn't it be better if we just told them we don't have anything here?" Trump said to one of his attorneys, according to the 49-page indictment.

Unauthorised disclosure of classified documents posed a risk to US national security, foreign relations, and intelligence gathering, prosecutors said.

The Justice Department made the criminal charges public on a tumultuous day in which two of Trump's lawyers, John Rowley and Jim Trusty, quit the case for reasons that were not immediately clear. A former aide, Walt Nauta, faces charges of being Trump's co-conspirator.

Trump is due to make a first appearance in the case in a Miami court on Tuesday, a day before his 77th birthday.

Since Trump would serve any sentences concurrently if convicted, the maximum prison time he would face is 20 years for obstruction of justice, a charge carrying the highest penalty.

"Our laws that protect national defense information are critical to the safety and security of the United States, and they must be enforced," US Special Counsel Jack Smith, who is leading the prosecution, said at a press conference.

"We have one set of laws in this country, and they apply to everybody," Smith said in his first public appearance since Attorney General Merrick Garland assigned him to the investigation last year.

Smith said he would seek a speedy jury trial in Florida. (Reuters)