Mueller's report revealed that President Donald Trump tried to seize control of the Russian Federation probe and force Mueller's removal to stop him from investigating potential obstruction of justice by the Republican president.
Mueller also announced the closure of his office after concluding in late March a two-year probe into Russian interference in the 2016 US presidential election and whether Trump had obstructed justice.
Barr said Mueller reached no conclusion on obstruction of justice by Trump so he and Deputy Attorney General Rod Rosenstein made their own finding that there wasn't evidence to make a criminal case against the president.
Lindsey Graham, a close ally of Trump's who chairs the Senate judiciary committee, meanwhile declared the case was closed, stating: "Mr Mueller has made a decision to move on and let the report speak for itself".
Joint Special Counsel / DOJ statement on the role of the OLC opinion.
"On the off chance that we had certainty that the president unmistakably did not perpetrate a wrongdoing, we would have said as much", Mueller said.
"'The Jews always flip", US President Donald Trump reportedly said after being told that three Jewish associates had agreed to cooperate with the Mueller probe, according to a new tell-all book on the Trump administration. "The case is closed".
His statement marks the end of the inquiry, which also sparked concerns on the reported unconstitutionality of charging a sitting United States president with a crime.
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After Mueller's statement, Trump tweeted, "Nothing changes from the Mueller Report".
"We did not, however, make a determination as to whether the President did commit a crime", he said. Barr dismissed the complaint as "a bit snitty" in testimony before the Senate Judiciary Committee.
Mueller said that long-standing Justice Department policy prohibits charging a sitting president with a federal crime.
"I will close by reiterating the central allegation of our indictments that there were multiple, systematic efforts to interference in our election", Mueller said as he wrapped up his statement on Wednesday.
The special counsel emphasised that his office had not ruled on whether US President Donald Trump had engaged in criminal conduct. The president has repeatedly and adamantly denied any claims of wrongdoing, including suggestions that he interfered with the special counsel's investigation. The summaries led to Trump's frequent tweets that Mueller found "NO COLLUSION and NO OBSTRUCTION!". "We chose those words carefully and the report speaks for itself", he said.
It will be Mueller's first statement on the report.
She added, "After two years, the special counsel is moving on with his life, and everyone else should do the same".
What matters is that Mueller can be fairly understood to be saying he believed President Trump committed obstruction of justice.