FORT PIERCE, Florida (Reuters) - Donald Trump continues his legal assault Friday on the criminal case accusing the former U.S. president of mishandling classified documents after leaving the White House, when his lawyers challenge the appointment of the prosecutor in the case.

Trump's lawyers during three days of hearings are also expected to argue against imposing a gag order on the Republican presidential candidate over his baseless claim that a standard FBI use-of-force policy included in papers related to the search of his Florida property for the documents was an authorization for them to assassinate him.

Trump's Republican allies in Congress have also voiced criticism of the appointment and funding of Special Counsel Jack Smith, who is leading the classified documents prosecution and a second criminal case in Washington accusing Trump of attempting to overturn his 2020 election defeat.

The hearings before U.S. District Judge Aileen Cannon, a Trump appointee, in Florida federal court will mark the first time his legal team has appeared in court since he was convicted on 34 felony counts in May of falsifying business records in New York.

Trump, who is challenging Democratic President Joe Biden in the Nov. 5 election, is also awaiting a landmark decision from the U.S. Supreme Court on his claims of presidential immunity in the election case.

Trump's lawyers face an uphill battle in challenging Smith's appointment. U.S. attorneys general serving presidents of both major political parties have appointed special counsels and courts have previously rejected challenges to their authority, most recently in cases involving Biden's son Hunter, who was found guilty this month on gun charges.

"It has been upheld every time it has come up," Kel McClanahan, a lawyer focused on national security issues, said of the special counsel authority. "It never works out" for the defense.

Trump has not raised the same challenge to Smith in the election case in Washington, where judges would be bound by prior rulings in prior challenges to special counsel.

TRUMP DENIES WRONGDOING

Trump faces ongoing criminal prosecutions including the documents case and two related to his attempts to overturn his 2020 defeat. He has pleaded not guilty in all three and has said without evidence that they are all attempts to stop him from returning to power.

Trump has argued in court filings in Florida that Smith did not have the authority to bring the charges because he was not confirmed by the Senate and his office was not created by an act of Congress. Trump's defense is also challenging the mechanism funding the prosecution.

Smith's office has disputed the claims and argued that his appointment is backed by prior court decisions.

Trump's legal challenges are part of a multi-pronged attack on Smith, whom Trump has called "deranged" and a "thug" on social media. Smith, a veteran public corruption prosecutor who worked on war crimes cases in The Hague, was named by Attorney General Merrick Garland in 2022 to lead the investigations into Trump.

His appointment was designed to give the probes a measure of independence from the Justice Department under the Biden administration.

Trump's challenge to Smith is one of a series of attempts by his lawyers to dismiss the classified documents charges. Cannon has indefinitely delayed the trial's start and it is unlikely the case will reach a jury before the November election.

The hearings will also address other issues including Trump's bid to suppress evidence seized during an FBI search of his Mar-a-Lago resort and Smith's request to bar Trump from making statements that may endanger law enforcement.

The request from Smith, which is scheduled to be discussed on Monday, came after Trump's baseless claims that FBI agents were authorized to assassinate him when they searched his Mar-a-Lago, Florida resort in August 2022.

Garland, who rarely speaks publicly about the Trump cases, has called Trump's claims "extremely dangerous."

Cannon has been receptive to Trump's defense on other issues and has signaled she may be open to Trump's arguments challenging Smith's appointment as special counsel.

In a rare move, she has allowed three outside lawyers representing legal experts and advocacy groups to argue during Friday's hearing. Two of those lawyers have filed court briefs siding with Trump in the dispute.

(Reporting by Andrew Goudsward; Editing by Scott Malone and Alistair Bell)

By Andrew Goudsward