New details of Donald Trump and his allies' "increasingly desperate" attempts to overturn the 2020 election have been outlined in a newly unsealed court filing from prosecutors in the landmark criminal case against the former president.

Trump intentionally lied to the public, election officials and his vice-president in his failed bid to cling to power, while privately describing election fraud claims as "crazy", prosecutors allege in the 165-page filing.

The filing from special counsel Jack Smith's team offers the most comprehensive view to date of what prosecutors intend to prove if the case charging Trump with conspiring to overturn the election reaches trial.

While Trump's efforts to undo the election have been chronicled in stark detail through a months-long congressional investigation, this filing cites previously unknown accounts by Trump's closest aides.

"The details don't matter," Trump said, when told by an adviser that a lawyer mounting his legal challenges wouldn't be able to prove the false allegations in court, the filing states.

The brief has been made public despite objections by Trump's legal team.

It comes in the final month of a closely contested presidential race.

Democrats have argued Trump is unfit for office, using his refusal to accept the election results four years ago to support their claim.

The topic surfaced as recently as this week's vice-presidential debate.

Tim Walz and JD Vance engaged in a minutes-long squabble over violence at the Capitol on January 6.

Mr Vance refused to directly answer when asked whether his running mate had lost the 2020 race.

The filing was initially submitted under seal in response to a Supreme Court opinion that conferred broad immunity on former presidents for official acts they take while in office.

The immunity decision narrowed the scope of the prosecution and eliminated the possibility of a trial before next month's election.

Prosecutors hope to persuade District Judge Tanya Chutkan that Trump's actions were undertaken in a private capacity, rather than under his role as president.

If they are successful, that would allow the charges to remain part of the case as it moves forward.

Judge Chutkan permitted a redacted version to be made public, despite Trump's lawyers arguing it was unfair to unseal it so close to the election on November 5.

It's uncertain whether the case will go to trial, particularly if Trump is elected president.

"Although the defendant was the incumbent President during the charged conspiracies, his scheme was fundamentally a private one," Mr Smith's team wrote.

"When the defendant lost the 2020 presidential election, he resorted to crimes to try to stay in office."

Trump campaign spokesman Steven Cheung argued the brief was "falsehood-ridden" and "unconstitutional".

He repeated claims that Mr Smith and Democrats were "hell-bent on weaponising the Department of Justice in an attempt to cling to power".

In a post to Truth Social, Trump said the case would end with his "complete victory".

The filing alleges Trump "laid the groundwork" for rejecting the election results before the contest was over.

He allegedly told advisers in the event he held an early lead, he would "declare victory before the ballots were counted and any winner was projected".

Prosecutors say immediately after the election, his advisers sought to sow chaos in the counting of votes.

In one instance, a campaign employee, who is also described as a Trump co-conspirator, was told results favouring Joe Biden at a Michigan polling centre appeared accurate.

The person is alleged to have replied, "find a reason it isn't" and "give me options to file litigation".