Donald Trump "resorted to crimes" in an effort to overturn his 2020 election defeat, prosecutors allege in a new court filing that argues the former president is not immune from charges.

Special Counsel Jack Smith, the prosecutor appointed to lead the election interference case against Trump, submitted the filing, which was publicly released on Wednesday.

The filing challenges Trump's claim that he is protected by a landmark Supreme Court ruling this summer that grants broad immunity from prosecution for official acts conducted while in office.

Since there will be no trial before Trump, a Republican, vies with his Democratic rival Kamala Harris for the White House in next month's election, the 165-page court document may be the last chance for prosecutors to outline their case.

In Wednesday's filing, prosecutors allege Trump was not always acting in an official capacity and instead engaged in a "private criminal effort" to overturn the 2020 results.

The document is an effort by prosecutors to advance the criminal case against Trump following the Supreme Court ruling in July.

It prompted prosecutors to narrow the scope of their indictment. That is because the ruling did not apply immunity to unofficial acts, leading prosecutors to argue that while Trump may still have been in office some of his alleged efforts to overturn the election were related to his campaign and his life as a private citizen.

The court should "determine that the defendant must stand trial for his private crimes as he would any other citizen," Mr Smith wrote in the new filing.

The case has been frequently delayed since charges were filed by the Department of Justice more than a year ago accusing Trump, who denies wrongdoing, of seeking to illegally block the certification of President Joe Biden's victory.

The filing lays out several instances in which Trump's Vice-President, Mike Pence, expressed doubt about his boss's voter fraud claims and tried to persuade him to accept he lost the election.

In the court document, prosecutors say Trump was not upset when he learned his vice-president had been rushed to a secure location as rioters stormed the Capitol on 6 January 2021. "So what?" he allegedly said, when informed of the scenes.

Pence would later go public about his falling out with Trump in the wake of the storming of Congress, when some rioters shouted "Hang Mike Pence" because the vice-president refused to obstruct the certification of election results.

Trump's lawyers fought to keep the latest filing sealed, and campaign spokesman Steven Cheung called it "falsehood-ridden" and "unconstitutional".

In a post on his Truth Social platform on Wednesday, Trump called it a "hit job" and said it "should not have been released right before the election".

He accused prosecutors of "egregious" misconduct.

The filing offers new evidence and presents the clearest view yet of how prosecutors would seek to present their case against Trump at trial.

It alleges that he always planned to declare victory no matter the result, and laid the groundwork for this long before election day. It also accuses him of knowingly spreading false claims about the vote that he himself deemed "crazy".

Mr Smith also provides several new details about the Trump campaign's alleged role in sowing chaos in battleground states, where a large number of mail-in ballots were being counted in 2020 because of the Covid-19 pandemic.

In the Democratic stronghold of Detroit, Michigan, when a large batch of ballots seemed to be in favour of Biden, a Trump campaign operative allegedly told his colleague to "find a reason" that something was wrong with the ballots to give him "options to file litigation".

The filing also claims that Trump and his allies, including lawyer Rudy Giuliani, sought to "exploit the violence and chaos at the Capitol" on 6 January 2021 to delay the election certification. They allegedly did this by calling senators and leaving voicemails that asked them to object to the state electors.

Trump said on Wednesday that the case would end with his "complete victory". A trial date has not been set.