The angry early morning outburst came after the release of the special counsel's findings revealed he had repeatedly attempted to obstruct justice, but that aides had refused to follow his instructions.
"Statements are made about me by certain people in the Crazy Mueller Report, in itself written by 18 Angry Democrat Trump Haters, which are fabricated & totally untrue," he said.
In what is thought to be the first example of a sitting president swearing in a tweet, he added: "Watch out for people that take so-called “notes,” when the notes never existed until needed.
"Because I never agreed to testify, it was not necessary for me to respond to statements made in the “Report” about me, some of which are total bullshit & only given to make the other person look good (or me to look bad)."
Mr Trump's tweet included an unfinished sentence and ellipsis at the end, usually suggesting a further post is to follow. But at the time of publication, two hours had passed from the "bullshit" tweet with no follow-up appearing on his feed.
While Mr Trump did not indicate which notes or statements he was objecting to, the 400-page Mueller report includes a series of embarrassing claims about the president. Some of those are said to be taken from contemporaneous notes, including the suggestion he described himself as "f**ed" when the probe began.
"Oh my God. This is terrible. This is the end of my Presidency. I’m fucked," he said, according to notes from Jeff Sessions’ then-chief of staff, Jody Hunt.
Mr Trump had initially attempted to present the Mueller report as a complete exoneration. Just before it was announced, he posted another tweet to his feed, addressed to his "haters" in which he referenced Game Of Thrones and wrote "Game Over" and "No Collusion. No Obstruction".
A further statement from Mr Giuliani and Mr Trump's lawyers said "the report itself is nothing more than an attempt to rehash old allegations" and insisted that "the results of the investigation are a total victory for the president".
Donald Trump Jr, the president's eldest son, was featured prominently in the report for meeting with a Kremlin-connected lawyer at TrumpTower in June 2016.
Although the report said "the campaign anticipated receiving derogatory documents and information" from Russians that "could assist Trump's electoral prospects", it said "the government would unlikely be able to prove beyond a reasonable doubt" that the participants at that meeting "had general knowledge that their conduct was unlawful".
The younger Trump tweeted a series of attacks on Democrats. "Better luck next hoax!" he said.
Senior White House adviser Kellyanne Conway said that because the White House did not interfere with Mr Mueller's work, that "should make people feel good about democracy".
"We're accepting apologies today, too," Ms Conway told reporters, adding that Mr Trump watched Mr Barr, talked to his lawyers and was in "a great mood".
The president, who normally talks to reporters on his way out of the White House, declined to speak as he left to spend the Easter weekend in Florida.
But from Air Force One, he tweeted: "I had the right to end the whole Witch Hunt if I wanted. I could have fired everyone, including Mueller, if I wanted. I chose not to. I had the RIGHT to use Executive Privilege. I didn't!"
Appearing relaxed earlier on Friday at a military event, Mr Trump said a statue he had been presented with as a memento would have a permanent home "at least for six years, in the Oval Office".
As the audience applauded and laughed, Mr Trump said he was going to joke and say "at least for 10 or 14 years, but we would cause bedlam if I said that".
Additional reporting by agencies
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