Mueller brought charges against 34 people and three companies during his investigation, with prison sentences for some of Trump's ex-aides such as former campaign chairman Paul Manafort and former personal lawyer Michael Cohen.
US Special Counsel Robert Mueller walks, after attending church, on March 24, 2019 in Washington, DC. Many of his opponents accused him of obstructing the Russian Federation probe when he fired former Federal Bureau of Investigation director James Comey.
He has attacked the Mueller investigation as a "witch hunt" more than 100 times, accused the special counsel of being conflicted, and disparaged his work nonstop.
It states: "While this report does not conclude that the president committed a crime, it also does not exonerate him".
Barr said the investigation also found insufficient evidence that Trump had attempted to obstruct justice.
"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", House Speaker Nancy Pelosi and Senate Minority Leader Chuck Schumer said in a joint statement.
The report was submitted on Friday to Attorney General William Barr, who has been poring over the document.
The headline finding was that no "Trump campaign official or associate conspired or knowingly co-ordinated" with operatives connected to the Russian government during the presidential campaign.
Mr Mueller, 74, found that Russian Federation sought to influence the election through misinformation pumped out on social media by a "troll farm" based in St Petersburg and by stealing and releasing emails from senior Democrats.More news: Nirav Modi: Billionaire jeweller arrested in London over India’s biggest banking fraud
They also raised questions about Barr's conclusion on obstruction of justice, citing a memo he sent to the Justice Department before his confirmation arguing it would be "fatally misconceived" that Trump's firing of FBI Director James Comey could be the basis of an obstruction of justice inquiry. That left it to the attorney general to decide.
Barr claimed in his letter that Mueller's decision against reaching any legal conclusions "leaves it to the Attorney General to determine whether the conduct described in the report constitutes a crime".
Barr said that Mueller "thoroughly" investigated the question of whether the Trump campaign coordinated with Russia's election interference, issuing more than 2,800 subpoenas, obtaining almost 500 search warrants and interviewing 500 witnesses.
Still, Attorney General William Barr's summary of Mueller's final report appeared to significantly reduce the risk of impeachment that had hovered over Trump nearly since he took office on January 20, 2017.
Kamala Harris, a senator from California, not only demanded "total transparency", but said Barr "must publicly testify under oath about the investigation's findings".
Trump, at his Mar-a-Lago, Fla., resort for the weekend, remained uncharacteristically silent about the completion of the investigation.
Congressional Democrats appeared stung by the failure of Mueller's report, after a 22-month investigation, to directly uncover presidential wrongdoing.
None of those charges, however, directly related to the question of collusion between the campaign and Moscow. "Trump told reporters afterwards that "hopefully, somebody's going to be looking at the other side".