Lawyers for Donald Trump say his attempts to cast doubt on the 2020 election fell within his official duties as president and are not subject to criminal prosecution.
The claims were "at the heart of his official responsibilities", they argue in a new filing.
The lawyers have asked a judge to dismiss the charges against him for alleged election interference.
Separately, they have asked for a delay in his classified documents case.
Mr Trump's attorneys have asked for the documents trial, in which the former president is accused of improperly handling sensitive files, to be held after the 2024 presidential election.
And in a case in New York, Mr Trump's attorneys requested the dismissal of 34 felony charges of falsifying business records.
Election interference
The charges relating to the 2020 election were brought in Washington DC by special prosecutor Jack Smith, who says Mr Trump interfered with the normal transfer of presidential power after his legal challenges to the vote were unsuccessful.
In that case, Mr Trump is charged with conspiracy to defraud the US, conspiracy to obstruct an official proceeding, obstruction of an official proceeding, and conspiracy against the rights of citizens.
Mr Trump has said that the charges against him - and all of the other legal cases against him and his companies - are politically motivated.
Classified documents
In the Florida classified documents case, which is also being prosecuted by Mr Smith's office, Mr Trump's attorneys have asked for a trial currently scheduled for May 2024 to be pushed back to at least mid-November.
That would put the start of the trial after next year's presidential vote on 5 November.
More than 325 classified files - including some marked "Secret" and "Top Secret" - were discovered at Mr Trump's Mar-a-Lago estate, some stored in a ballroom, others in a bathroom and a shower.
Mr Trump's lawyers contend that they have not yet had adequate access to classified material and witness statements, and have previously argued that it would be impossible to hold a fair trial in the midst of a presidential campaign.
Business records
Mr Trump's request to dismiss charges of falsifying business records was publicly released on Thursday, after his lawyers filed the motion last week.
The New York case stems from his payment of $130,000 (£105,000) to adult film actress Stormy Daniels, who says she was paid to stay quiet after having sex with him.
Prosecutors allege Mr Trump illegally altered records in order to claim that the payment was for legal fees.
In the legal filing, his lawyers call the case a "five-year meandering, halting, and roving investigation that entailed inexplicable and unconstitutional delay" and argue that the charges are a novel interpretation of the law and "politically driven".
Ongoing legal issues
Trump also faces criminal charges in Georgia related to his attempts to overturn the 2020 election result.
The fraud trial against him, two of his sons and the Trump Organization which began this week in New York is a civil, not criminal, action. It could result in a fine, a ban on doing business in New York state, and loss of control of his companies.
He also faces a defamation suit by writer E Jean Carroll, after a jury found him liable for sexually abusing her in the mid-1990s and later lying about it.
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