“There was no collusion with Russia. There was no obstruction. It was a complete and total exoneration,” Trump said of Mueller’s conclusions.

“It’s a shame that the country had to go through this,” he added.

“This was an illegal takedown that failed.”

Deputy press secretary Hogan Gidley said Trump was “in a really good mood” and “very happy with how it all turned out.”

The president watched television, talked to staff and made calls during his flight home from Florida.

Back at the White House, Trump said only: “I just want to tell you that, America is the greatest place on earth, the greatest place on Earth.”

Summarising Mueller’s findings, Barr said no Trump campaign official was involved in Russian conspiracies in 2016 to hack Democratic computers and flood social media with disinformation to harm Trump’s Democratic election rival Hillary Clinton.

He also said there were no new surprises coming from the Mueller team, which is disbanding - no further indictments being referred, and no sealed indictments outstanding.

On the other hand, according to Barr’s letter, Mueller clearly had some evidence to support an obstruction case, but was uncertain whether it was enough to support criminal charges.

“While this report does not conclude that the president committed a crime, it also does not exonerate him,” Barr cited Mueller as saying.

Democrats in Congress are now certain to demand Mueller’s underlying evidence and push to investigate further.

Nevertheless, a major barrier for Trump’s re-election in 2020 lifted just as a strong field of potential Democratic candidates was forming to select who would take him on.

Trump for two years has labelled the investigation a “witch hunt”, even as Mueller’s team issued charges ranging from conspiracy to lying to investigators against 34 individuals.

Six of those were former insiders in Trump’s circle, and five have been convicted, including Trump’s former personal attorney Michael Cohen, his national security advisor Michael Flynn and his campaign chairman Paul Manafort.

Cohen was sentenced to three years in prison for crimes including, at Trump’s alleged instruction, using campaign funds for hush payments to an adult film star who allegedly had an affair with Trump.

And Manafort was imprisoned for 7.5 years, though mostly for crimes unrelated to the campaign.

The unending probe saw Trump frequently angrily attacking Mueller - one of the most respected members of Washington’s judicial and prosecutorial elite - and at times appeared to throw his policy momentum off course.

Paul Manafort charged in New York: is this Robert Mueller’s secret weapon against a Donald Trump pardon?

For months, the White House worried that Mueller was honing in on Trump’s family, including son Don Jnr and son-in-law Jared Kushner, as well as Trump himself.

And it also left questions in the minds of many of his supporters, who will now likely unite around his declaration of “complete exoneration”.

White House advisor Kellyanne Conway tweeted “congratulations” to her boss.

“Today you won the 2016 election all over again. And got a gift for the 2020 election,” she tweeted.

“They’ll never get you because they’ll never ‘get’ you.”

But the end of Mueller’s operation did not leave Trump’s White House in the clear.

Democrats in Congress are already conducting some 17 investigations of the administration, spreading their net far more broadly than Mueller’s relatively narrow mandate.

They want the full Mueller report and they are demanding the underlying evidence supporting his conclusions.

Senate Democratic Leader Chuck Schumer and House Speaker Nancy Pelosi said Barr’s summary of the Mueller findings “raises as many questions as it answers”.

“The fact that Special Counsel Mueller’s report does not exonerate the president on a charge as serious as obstruction of justice demonstrates how urgent it is that the full report and underlying documentation be made public without any further delay,” they said.

“And most obviously, for the president to say he is completely exonerated directly contradicts the words of Mr Mueller and is not to be taken with any degree of credibility.

Democrat Jerry Nadler, chairman of the House Judiciary Committee, announced that he would be calling Barr to testify in the near future.

“Special Counsel Mueller clearly and explicitly is not exonerating the president, and we must hear from AG Barr about his decision making and see all the underlying evidence for the American people to know all the facts,” Nadler said.

The Mueller investigation: five takeaways

● Mueller’s investigation did not establish that US President Donald Trump’s campaign conspired or coordinated with Russia to interfere in the 2016 US presidential election.

●The special counsel left unresolved questions about whether the president obstructed justice. Barr concluded the evidence was “not sufficient to establish that the president committed an obstruction of justice offence.”

●With the 2020 election campaign under way, the political fight continues in Washington. The Republican Trump said he had been completely exonerated and Democrats, conducting their own investigations in the House of Representatives, challenged him on that statement and demanded to see Mueller’s full report.

●Mueller ended his investigation on Friday after bringing charges against 34 people, including Russian agents and former key Trump allies such as campaign chairman Paul Manafort, national security adviser Mike Flynn and personal lawyer Michael Cohen, although none of those charges directly related to whether Trump’s campaign worked with Moscow to influence the election outcome.

●Trump’s legal woes are far from over, with the US Attorney’s office in Manhattan and other prosecutors pursuing cases that include possible campaign finance violations. Prosecutors have said Trump directed Cohen to make hush-money payments to women who said they had sex with Trump. Trump denies having had sexual relationships with the two women: Stormy Daniels, the porn actress whose real name is Stephanie Clifford, and former Playboy model Karen McDougal.

Prosecutors are also examining potential illegal donations to Trump’s inauguration committee.

Additional reporting by Reuters and Associated Press