In their brief filed on Monday, Smith and his team of lawyers urged the Atlanta-based US Court of Appeals for the 11th Circuit to overturn the July 15 ruling by US District Court Judge Aileen Cannon in which she concluded that Smith was unlawfully appointed and did not have the legal authority to bring the case.
"Congress has bestowed on the attorney-general, like the heads of many Executive Departments, broad authority to structure the agency he leads to carry out the responsibilities imposed on him by law," they wrote.
"The district court's contrary view conflicts with an otherwise unbroken course of decisions, including by the Supreme Court, that the Attorney-General has such authority, and it is at odds with widespread and longstanding appointment practices in the Department of Justice and across the government."
The Department of Justice had previously said it planned to appeal the ruling.
Donald Trump's lawyers have asked to have Special Counsel Jack Smith latest request rejected. (AP PHOTO)
In Monday's brief, Smith's office also asked the appellate court to schedule oral arguments.
Cannon, who was appointed to the bench by Trump, found Attorney-General Merrick Garland's decision to appoint Smith in 2022 violated the US Constitution. She also found that his budget, which is funded through an indefinite appropriation, was unlawful.
Trump's lawyers had previously challenged the legal authority for Smith's appointment, arguing that Smith's office was not created by Congress and the special counsel was not confirmed by the Senate.
Trump's campaign on Monday said the court should reject Smith's request and that other cases facing the former president should be dismissed.
"Not only should the dismissal of the Lawless Indictment in Florida be affirmed, but be immediately joined by a dismissal of ALL the Witch Hunts. The Democrat Justice Department coordinated ALL of these Political Attacks, which are an Election Interference conspiracy against Comrade Kamala's Political Opponent, President Trump. Let us come together to END all Weaponisation of our Justice System," Trump campaign spokesman Steven Cheung said in a statement.
Cannon's ruling has faced staunch criticism, with many lawyers saying it flies in the face of prior court decisions which all upheld the legality of the rules that the Justice Department has relied on for years in appointing special counsels.
"The attorney-general validly appointed the Special Counsel, who is also properly funded," Smith's office wrote, adding that Cannon had "deviated from binding Supreme Court precedent" and also "misconstrued the statutes that authorised the Special Counsel's appointment".
Cannon's decision to dismiss the case marked a legal victory for Trump, and came not long after the Supreme Court ruled that he had broad criminal immunity from prosecution for official actions he took during his time in office.
That Supreme Court decision has led to major delays in Smith's second criminal case against Trump, in which Trump is facing charges over his efforts to overturn the results of 2020 presidential election.
Smith faces a Friday deadline to tell the judge overseeing the election subversion case how he wishes to proceed in light of the Supreme Court's ruling.
Trump, who is running in the 2024 presidential election against Vice President Kamala Harris, was convicted in May on New York state charges involving hush money paid to a porn star to avert a sex scandal before the 2016 election.
His sentencing has been postponed following the Supreme Court's ruling on presidential immunity.
In the documents case, Trump was indicted on charges that he wilfully retained sensitive national security documents at his Mar-a-Lago estate in Florida after leaving office in 2021 and obstructed government efforts to retrieve the material.
