Other Eastern European countries, such as Bulgaria, were also targeted, as well as NATO and the Organization for Security and Cooperation in Europe (OSCE).
Russian President Vladimir Putin has repeatedly poured scorn on North Atlantic Treaty Organization (NATO). According to FireEye, hacking NATO could give Moscow, "sensitive tactical and strategic intelligence concerning regional military capabilities and relationships".
The report comes amid heightened tension between the West and Russia, following Moscow's annexation of Crimea in March. The finger has been pointed at Russia for several widely reported cyberattacks, including a breach at JPMorgan that compromised the accounts of 76 million households and seven million small businesses.
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In addition, cyber intelligence firm iSight Partners has recently reported that Russian hackers exploited a vulnerability in Microsoft Windows to spy on computers used by Nato and other western governments.
Attacks likely successful
FireEye said that the sophistication of the attacks detailed in its report meant that they were likely to have proved successful in the majority of cases.
"I think you would be naïve to assume they haven't been successful. For the large percentage of hacks they are successful, because we know existing security architecture is insufficient in stopping these things," Jason Steer, director of technology strategy at FireEye, told CNBC by phone.
Identifying where hackers are from can be difficult because of clever movement of data and deliberately misleading use of language in malware. Russia is particular hard to pin down due to its hackers covert movements in cyberspace, said Steer.
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"They are more adept at covering their trail and they don't want to be seen to be aggressive and active in the way China are, as it could impact negotiations with the European Union and other trading bodies," he said.
FireEye identified APT28 as Russian, based on malware samples that had Russian language settings and which were employed during the working hours of Russia's major cities.
Like Russia, China has also been accused of cyberespionage. Earlier this year, five Chinese military hackers were indicted by U.S. authorities for corporate espionage.