It was the first time a US president had been convicted of or charged with a criminal offence.
MrTrump had tried to cover up “hush money” payments to a porn star in the days before the 2016 election.
When Stormy Daniels‘ claimsof a sexual liaison threatened to upend his presidential campaign, Trump directed his lawyer to pay $130,000 (£102,000) to keep her quiet.
A judge delayed Mr Trump’s scheduled 26 November sentencing indefinitely last month to give him the chance to seek dismissal.
A dismissal would erase Mr Trump’s historic conviction, sparing him of a criminal record and possible prison sentence.
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The judge could also decide to uphold the verdict and proceed to sentencing, delay the case until Mr Trump leaves office, wait until a federal appeals court rules on Trump’s parallel effort to get the case moved out of state court or choose some other option.
The president-elect’s lawyers argue having the case loom over his four-year presidential term that begins on 20 January would cause “unconstitutional impediments” to his ability to govern.
Prosecutors have until 9 December to respond.
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Starmer on relationship with Trump
The filing references the pardon Joe Biden issued to his son on Monday, in which the president said Hunter Biden was “unfairly prosecuted” on gun and tax charges.
Mr Trump’s lawyers said: “President Biden argued that ‘raw politics has infected this process and it led to a miscarriage of justice’. These comments amounted to an extraordinary condemnation of President Biden’s own DOJ [department of justice]”.
The Manhattan District Attorney Alvin Bragg “has engaged in ‘precisely the type of political theatre’ that President Biden has condemned”, the filing added.
“This case is based on a contrived, defective, and unprecedented legal theory relating to 2017 entries in documents that were maintained hundreds of miles away from the White House where President Trump was running the country.”
The district attorney’s “disruptions to the institution of the presidency violate the presidential immunity doctrine because they threaten the functioning of the federal government,” the filing said.
The prosecutors’ “ridiculous suggestion that they could simply resume proceedings after President Trump leaves office, more than a decade after they commenced their investigation in 2018, is not an option,” the filing claimed.
Mr Trump’s lawyers also claimed the case should be thrown out because of his “extraordinary service” to the US, adding that his “civil and financial contributions to this city and the nation are too numerous to count”.
The president-elect has said he intends to nominate the lawyers who wrote the filing – Todd Blanche and Emil Bove – to top jobs in the justice department, which they criticise in the documents.