Data from the laptop showed it was also present in the Swiss city of Lausanne where it was linked to the hacking of a laptop belonging to the World Anti-Doping Agency (Wada), which has exposed doping by Russian athletes.
The Australian government added that Russia's actions violated its global commitments to "responsible state behaviour" in cyberspace.
The U.S. Justice Department has charged seven Russian military intelligence officers with hacking anti-doping agencies and other organizations.
The indictments were announced as Dutch security services said they had thwarted a cyber attack on the global chemical weapons watchdog, the OPCW - expelling four Russian agents - and after Britain and Australia blamed the GRU for plots that notably targeted the US Democratic Party and global sports bodies.
Four Russian officers of the Main Directorate of the General Staff of the Armed Forces of the Russian Federation, GRU, are escorted to their flight after being expelled from the Netherlands for allegedly trying to hack into the United Nations chemical watchdog OPCW's network.
British government sources said they had has assessed with "high confidence" that the GRU was "almost certainly" behind the Democratic Party hack that some Hillary Clinton supporters claimed helped tip the USA election in Donald Trump's favour, as well as the WADA attack which resulted in the release of the medical files of global sports stars including tennis's Serena and Venus Williams and British cyclist Bradley Wiggins.
"We are ready today to provide cyber support to our allies, I've seen enough of the evidence to say that the Dutch and the British are 100 per cent accurate in who they have attributed this to", Mattis said.
NATO's chief vowed on Thursday to strengthen the alliance's defences against attacks on computer networks that Britain said are directed by Russian military intelligence, also calling on Russia to stop its "reckless" behaviour.
"NATO will continue to strengthen its defence and deterrence to deal with hybrid threats, including in the cyber domain", he added as North Atlantic Treaty Organisation defence ministers met to discuss new offensive cyber capabilities.
It cites attacks on the World Anti-Doping Agency, Ukrainian transport systems, the 2016 USA presidential race and others as very likely the work of the GRU.
Russia's foreign ministry spokeswoman Maria Zakharova said that the allegations had been mixed together "indiscriminately".
Four of the names in the indictment match those given by Dutch authorities in connection with an alleged GRU cyberoperation against the Organisation for the Prohibition of Chemical Weapons, an worldwide chemical weapons watchdog organization based in the Netherlands.
In part, the double exposure of the GRU - first wandering around Salisbury in search of the doorknob of Sergei Skripal's home, and then caught in a carpark in the The Hague hacking into the chemical weapons watchdog - has simply been made possible by Russian incompetence.
LONDON-The British government has accused Russian military intelligence of being behind four cyber attacks aimed at spreading confusion and disinformation. Russian Federation has repeatedly denied the charges.
The building of the Organisation for the Prohibition of Chemical Weapons (OPCW) is pictured in The Hague, Netherlands, on October 4, 2018.
The cyber attacks were revealed in an unprecedented fight back by the Dutch, British and U.S. authorities who outed four GRU spies detained in The Hague this year.
According to John Demers, the assistant attorney general for national security, members of the Russian military intelligence agency GRU engaged in a hacking conspiracy to obtain nonpublic health information about athletes and others in the anti-doping files of multiple sports organizations in the US and overseas.
The "close access" hacking attempt, just a month after the Salisbury nerve agent attack, followed an earlier failed "spearfishing attack" on the OPCW headquarters.
The U.S. Treasury said in March that the GRU "knowingly engages in significant activities that undermine cybersecurity on behalf of the Russian government".