US President Donald Trump has declared "Game Over" for his "haters" - but a long-awaited report revealed how he sought the firing of the man investigating his team's alleged links to Russia.

A redacted 448-page, two-volume report of special counsel Robert Mueller's inquiry, published on Thursday, set out multiple episodes in which Mr Trump directed others to influence the Russia probe.

Among those was the disclosure of how the president urged an aide to instigate the sacking of Mr Mueller himself.

In June 2017 - a month after Mr Mueller's appointment to probe possible cooperation between Mr Trump's 2016 election campaign and Moscow - the president attempted to remove Mr Mueller from his position, the report said.

The lengthy document described how Mr Trump called White House lawyer Don McGahn and told him to call then-attorney general Jeff Sessions to say Mr Mueller "had conflicts of interest and must be removed".

"McGahn did not carry out the direction, however, deciding that he would resign rather than trigger what he regarded as a potential Saturday Night Massacre," the report added, referencing the firing of key officials during former president Richard Nixon's Watergate scandal.

Mr Mueller's 22 month-long work focused on Russian hacking and social media campaigns, possible Russian government links to - and contacts with - the Trump campaign, and potential obstruction of his investigatory efforts.

US Attorney-General William Barr testifying before a Subcommittee on Commerce, Justice, Science, and Related Agencies, in Washington DC | Image: Liu Jie/Xinhua News Agency/PA Images

Mr Trump's efforts to influence the investigation "were mostly unsuccessful, but that is largely because the persons who surrounded the president declined to carry out orders or accede to his requests," Mr Mueller wrote.

Although he did not conclusively find that Mr Trump had committed criminal obstruction of justice, Mr Mueller did not exonerate the president on the question either.

He found no evidence of collusion between Mr Trump's campaign team and Russia - despite "numerous links" - but said the president's campaign "expected it would benefit electorally from information stolen and released through Russian efforts", referring to hacked Democrat emails.

Other explosive findings in Mr Mueller's highly-anticipated report included:

• Mr Trump's belief that Mr Mueller's appointment as a special counsel to investigate possible Russia links would "end" his spell in the White House. "Oh my God. This is terrible. This is the end of my presidency. I'm f****d," Mr Trump said, according to the report
• There was "substantial evidence" that Mr Trump fired James Comey as FBI director in 2017 due to his "unwillingness to publicly state that the president was not personally under investigation"
• Written answers from Mr Trump to questions by Mr Mueller's team were considered "inadequate", but they decided against trying to compel Mr Trump to give evidence in person due to the likelihood of a long legal battle
• Mr Trump "launched public attacks on the investigation and individuals involved in it who could possess evidence adverse to the president, while in private, the president engaged in a series of targeted efforts to control the investigation", the report said

To cheers at a White House event following the release of Mr Mueller's report, Mr Trump said he was having a "good day" and declared "no collusion, no obstruction".

He added: "There never was, by the way, and there never will be.

"This should never happen to another president again, this hoax."

The president had earlier posted an image, inspired by TV series Game of Thrones, on Twitter with the same "no collusion, no obstruction" message.

His tweet added: "For the haters and the radical left Democrats - Game Over."

The president's legal team also hailed a "total victory" and claimed there had been "unprecedented cooperation" by Mr Trump with the special counsel's work.

However, Mr Trump did not repeat his claim - made last month when Mr Mueller disclosed in a summary of his report that the president nor his team conspired with Russia to win the 2016 election - that he had been granted a "complete and total exoneration".

Mr Trump's political rivals urged the US public to ignore the "spin" over Mr Mueller's report.

Invitations also flew in for Mr Mueller to testify before various US Congress committees on the results of his investigation.

Jerrold Nadler, the Democrat chair of the House of Representatives' judiciary committee, requested Mr Mueller to appear before his panel "no later than 23 May".

READ @HouseJudiciary Chairman @RepJerryNadler on the Mueller Report: Even in its incomplete form, the Mueller report outlines disturbing evidence that President Trump engaged in obstruction of justice. Just imagine what remains hidden from our view.https://t.co/eTLiUCZioQ

— House Judiciary Dems (@HouseJudiciary) April 18, 2019

The bullishness of Mr Trump in asserting "no obstruction" came despite US Attorney-General William Barr revealing Mr Mueller's report recounted "10 episodes" involving the president and discussed "potential legal theories for connecting these actions to elements of an obstruction offence".

However, Mr Barr himself used a news conference before the report's publication to reveal his own conclusion that "the evidence developed by the special counsel is not sufficient to establish that the president committed an obstruction-of-justice offence".

The Attorney-General, the replacement for Mr Sessions who was sacked by Mr Trump last year, also claimed the "unprecedented situation" faced by the president should be taken into account when assessing his actions.

Mr Barr said: "As he entered into office, and sought to perform his responsibilities as president, federal agents and prosecutors were scrutinising his conduct before and after taking office, and the conduct of some of his associates.

"At the same time, there was relentless speculation in the news media about the president's personal culpability."

Senator Kirsten Gillibrand, a senior Democrat, branded Mr Barr's news conference "a complete farce and an embarrassing display of propaganda on behalf of President Trump".

Democrat Senate leader Chuck Schumer and House of Representatives speaker Nancy Pelosi said in a joint statement: "The differences are stark between what Attorney General Barr said on obstruction and what Special Counsel Mueller said on obstruction.

"As we continue to review the report, one thing is clear: Attorney General Barr presented a conclusion that the president did not obstruct justice while Mueller's report appears to undercut that finding."

They both also called for Mr Mueller to provide public testimony to both houses of US Congress "as soon as possible".

Read my full statement with @SenSchumer – including a description of several of the ways Attorney General Barr misled the public – here: https://t.co/rzIylA2MoH

— Nancy Pelosi (@SpeakerPelosi) April 18, 2019