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Some non-sensitive data was posted online in October by a Twitter account that took credit for stealing the information, Mueller's office said in a court filing.
The data that appeared online was "altered and disseminated as part of a disinformation campaign aimed (apparently) at discrediting ongoing investigations into Russian interference in the US political system," prosecutors wrote.
The illicit activity outlined by prosecutors illustrates the concerns by US intelligence officials about continuing efforts by Russia to interfere in US politics.
The Russian firm, Concord Management and Consulting LLC, is being prosecuted in Mueller's investigation of US allegations that Moscow meddled in 2016 to undermine the American democratic process and help then-Republican candidate Donald Trump defeat Democrat Hillary Clinton.
Mueller is also investigating whether there was any coordination between members of the Trump campaign and Moscow officials. The Kremlin denies election interference and President Trump denies there was any collusion, calling the inquiry a political witch hunt.
Wednesday's filing in the US District Court for the District of Columbia is the latest in a dispute between prosecutors and Concord's American attorneys over whether the defense team can share highly sensitive evidence with Concord's corporate officers in Russia.
One of those officers is businessman Evgeny Prigozhin, an associate of Russian President Vladimir Putin and known in Russia as "Putin's cook."
In an indictment last year, Mueller's office said Russian defendants adopted false online personas to push divisive messages, traveled to the United States to collect intelligence and orchestrated political rallies while posing as Americans. Prigozhin was indicted in the same case along with 12 other people.