But the details of the Mueller Report paint a starkly different picture on the question of whether the President sought to fire Special Counsel Mueller, as Mr. Trump's claims run directly counter to the testimony of McGahn and other aides and advisers.
McGahn, who reportedly spoke with investigators for 30 hours about the Russia investigation, testified that the President called him on June 17, 2017 - about a month after Mueller had been named as Special Counsel - and pressed for Mueller to be ousted, an order that McGahn repeatedly ignored.
"McGahn recalled the President telling him 'Mueller has to go' and 'Call me back when you do it,'" the Mueller report described on page 300.
"McGahn is a credible witness with no motive to lie or exaggerate given the position he held in the White House," Mueller concluded, saying there was 'substantial evidence' that President Trump 'in fact directed McGahn to call (Rod) Rosenstein to have the Special Counsel removed."
The Mueller Report also says that after news reports surfaced in 2018 that the President had ordered the firing of Mueller, McGahn was asked to publicly dispute those reports - and McGahn refused.
"McGahn told (White House aide Rob) Porter that the President had been insistent on firing the Special Counsel," as McGahn testified that he told Porter the media reports were true.
McGahn testified that President Trump had talked of "knocking out Mueller" as early as a May 23, 2017 telephone call, just days after Mueller had been named as the Special Counsel.
The report says the President discussed firing Mueller with a number of people - not just McGahn - including former New Jersey Gov. Chris Christie, as well as White House Chief of Staff Reince Priebus and top aide Steve Bannon.
"You gotta do this," McGahn quoted the President as saying, as footnotes in the Mueller Report refer not only to McGahn's own notes and phone logs, but also calls listed in the 'President's Daily Diary.'
The President's tweets came as the White House is reportedly raising objections to possible testimony before Congress by McGahn - the House Judiciary Committee has already sent McGahn a subpoena for a May 21 appearance.
Democrats said the basic question is simple - either McGahn or the President is telling the truth - but not both of them.
"Trump now claims that White House Counsel Don McGahn lied under oath to the Special Counsel," said Rep. Don Beyer (D-VA), as Democrats immediately questioned the President's claim about McGahn.
"And if you aren't lying, then why are you preventing Don McGahn from testifying?" tweeted Rep. Ted Lieu (D-VA).