Mr Barr took the decision after special counsel Robert Mueller, who led the probe, declined to draw a legal conclusion about the president’s conduct.
The special counsel’s team, according to Mr Barr, undertook a “thorough factual investigation” into whether Mr Trump’s actions could constitute obstruction of justice.
“While this report does not conclude that the President committed a crime, it also does not exonerate him,” Mr Mueller is quoted as saying in his report, which was delivered to the attorney general on Friday after an investigation which lasted nearly two years.
Mr Mueller’s decision allowed the attorney general to make a ruling instead.
“Deputy attorney general Rod Rosenstein and I have concluded that the evidence ... is not sufficient to establish that the president committed an obstruction of justice offence,” Mr Barr wrote in a summary of the report, which was sent to members of the House Judiciary Committee on Sunday.
The special counsel’s investigation also did not find that collusion took place between the Trump campaign and the Russian government's election interference efforts.
Mr Barr, a political appointee, wrote that the report he received was divided into two main parts addressing whether Mr Trump’s campaign conspired with Russia during the 2016 election, and whether Mr Trump obstructed justice with his actions during the investigations that have followed.
The special counsel’s report concluded that there were two primary ways in which Russian forces attempted to influence the 2016 election.
One of those included a disinformation campaign online and in social media “to sow social discord” with the intent of influencing the campaign, and conducted by the Russian group the Internet Research Agency.
The second Russian strategy aimed at influencing the 2016 campaign was a computer hacking campaign, which successfully stole emails from the 2016 campaign of Hillary Clinton and the Democratic National Committee before those documents were published by WikiLeaks.
According to Mr Barr’s summary, the report indicated that investigators did not find that the Trump campaign or officials co-ordinated with that effort “despite multiple offers from Russian-affiliated individuals to assist the Trump campaign”.
The full report has not been made public but the White House said it was a “total and complete exoneration” of Mr Trump.
“It’s better than I expected,” Rudy Giuliani, a lawyer for the president, said.
Some members of Congress criticised the attorney general’s decision to make a ruling on obstruction of justice where the special counsel had declined to.
“In light of the very concerning discrepancies and final decision making at the Justice Department following the Special Counsel report, where Mueller did not exonerate the President, we will be calling Attorney General Barr in to testify,” Jerry Nadler, the chair of the House Judiciary Committee, said.
Mr Trump began posting on his Twitter account after the report summary was made public.
“No Collusion, No Obstruction, Complete and Total EXONERATION,” he said. “KEEP AMERICA GREAT!”
Shortly afterwards he spoke to reporters and said: “To be honest it’s a shame that your president has had to go through this.” He described the investigation as an “illegal takedown that failed” and added that “hopefully somebody’s going to be looking at the other side,” he added.
Additional reporting by agencies