In a four-page letter to Congress, Barr said in March that Mueller "did not find that the Trump campaign or anyone associated with it conspired or coordinated with Russia in its efforts to influence the 2016 US presidential election."
Barr's letter also said the Special Counsel withheld judgment on whether Trump tried to obstruct justice during the investigation.
"The Special Counsel . . . did not draw a conclusion - one way or the other - as to whether the examined conduct constituted obstruction," Barr wrote. "The Special Counsel states that 'while this report does not conclude that the President committed a crime, it also does not exonerate him.' "
Barr and his deputy, Rod Rosenstein, examined the obstruction evidence laid out by Mueller's team and concluded it did not rise to the level of obstruction of justice.
Since those findings were announced, congressional Democrats have been sharply critical of Barr's handling of the Mueller report, accusing the attorney-general of soft-pedalling the findings to protect the president.
The House Judiciary Committee is poised to issue a subpoena for the report's redacted portions.
As Barr's standoff with House Democrats continues, at least one influential Republican - Representative Devin Nunes - has signed on to an effort to demand that the Attorney-General provide the House Intelligence Committee with any redacted intelligence and counterintelligence information Mueller considered in compiling his report.
In a letter to Justice Department leaders dated March 27 but made public only today, Nunes and Representative Adam Schiff, D, cited laws that entitle the Intelligence Committee to review such information. Schiff is the panel's chairman, Nunes its top Republican.
In their letter, Nunes and Schiff requested "all materials, regardless of form and classification, obtained or produced by the Special Counsel's office in the course of the investigation" - while also insisting that the Justice Department make Mueller and the senior staff who worked with him available to brief the committee.
Barr has spent weeks redacting sensitive information from the report in preparation for its public release.
Barr is shielding four specific categories of information: grand jury material, details whose public release could harm ongoing investigations, any information that would "potentially compromise sources and methods" in intelligence collection, and anything that would "unduly infringe on the personal privacy and reputational interests of peripheral third parties."
That last category of redaction suggests Barr wants to keep secret any derogatory information gathered by investigators about figures who ended up not being central to Mueller's investigation.