It also said that it is ready to improve ties with the United States but it's up to Washington to make the first move.
Kremlin spokesperson Dmitry Peskov told journalists he had not seen the report but Russsias's "principled position on this matter is well known; our country has not interfered in the domestic affairs of other countries, including the United States," news agency AFP reported.
Peskov insisted "the accusations of interference... that are still being made against Russia, we as before consider to be baseless."
In Russia, pro-Kremlin lawmakers hailed the report as vindicating both Russia and Trump.
The report's findings "are a disgrace for the US and its political elite," Senator Alexei Pushkov wrote on Twitter.
"There's a chance to start a lot again from zero in our relations, but whether Trump will take the risk is still under question. We, of course, are ready," Konstantin Kosachev, foreign affairs committee chair in the upper house of parliament, wrote on Facebook.
In a letter sent to Congress summarising Mueller report, Barr quoted Special Counsel saying, "While this report does not conclude that the president committed a crime, it also does not exonerate him."
Barr said the investigation did not recommend any further indictments and does not have any further sealed indictments outstanding.
In his own review of Mueller's findings on obstruction -- one of the most explosive allegations against Trump -- Barr said, "the evidence... is not sufficient to establish that the president committed an obstruction-of-justice offence."
Barr's letter marked the conclusion of the 22-month investigation by Mueller, a former FBI director, into allegations that Trump's election campaign coordinated and colluded with Russians to skew the 2016 vote so the billionaire real estate magnate would win.
But it marked the beginning of a new phase, the determination of Democrats in Congress to further investigate Trump, using the evidence from the Mueller probe.