Australia has joined allies in publicly accusing the Russian government of mounting an "indiscriminate and reckless" campaign of cyber attacks against democracies.

The British government on Thursday said the GRU – the intelligence arm of Russia's military – is responsible for malicious cyber warfare targeting political, business, media and sporting institutions in violation of international law.

The campaign affected many countries and caused millions of dollars of economic harm, a statement from Prime Minister Scott Morrison and Foreign Minister Marise Payne said, pointing to advice from intelligence agencies.

The Kremlin orchestrated a campaign of global cyber attacks, according to Western allies. Credit:AP

"This is unacceptable and the Australian government calls on all countries, including Russia, to refrain from these types of malicious activities," Mr Morrison and Senator Payne said.