A federal judge has rejected a bid by Donald Trump to throw out a criminal case that charges him with illegally holding on to classified documents after leaving the White House.

US District Judge Aileen Cannon issued the ruling after a day-long hearing in Florida during which the former president’s lawyers argued the Espionage Act is too vague to be used against him.

“It’s difficult to see how this gets you to dismissal of the indictment,” she told his lawyers at one point.

The judge also indicated she was unlikely to agree to a separate request by Mr Trump to dismiss the case on the grounds he had deemed the documents to be “personal” rather than government property.

As Mr Trump looked on in the courtroom, his legal team pressed Ms Cannon to throw out the case.

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Donald Trump arrives for the hearing in Fort Pierce, Florida. Pic: Reuters

The Presidential Records Act gave him the authority to designate the records he took with him to his Mar-a-Lago estate in Florida as personal property, his legal team argued.

However, prosecutors argued the records were clearly presidential, not personal, and included top-secret information and documents related to nuclear programmes and the military capabilities of the US and foreign countries.

Ms Cannon’s ruling on Thursday covered only the Espionage Act arguments.

A decision on the separate motion regarding the Presidential Records Act remains pending.

That issue could be addressed during the trial, the judge said. She is yet to announce when it will take place.

Prosecutors have pressed the judge to set a date for this summer, while Mr Trump’s lawyers are hoping to put it off until after the presidential election.

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After the hearing, Mr Trump said on his Truth Social platform that he took note of the “big crowds” outside the courthouse, which included supporters with flags and signs who honked their car horns in solidarity with the ex-president. He again said the prosecution is a “witch hunt” inspired by President Joe Biden.

It is one of four criminal cases he faces as he tries to win back the White House.

The former president is also facing charges in relation to the riots at the US Capitol after the last presidential election, and over allegations he arranged payments to a porn actress.

The fourth case relates to accusations he criminally conspired to overturn his narrow defeat in the state of Georgia in the 2020 election.