Documents already released have proved a major headache for Canberra, sparking its worst diplomatic crisis in years with neighbour Indonesia amid warnings that more revelations appear likely. (Agencies)
An Australian newspaper said that the vast scale of the security breach is only just becoming evident.
It reported that intelligence agencies had determined that between 15,000 and 20,000 secret Australian files could have been accessed by Snowden through his computer at America's National Security Agency.
Though it was not known how many of them he actually stole before seeking refuge in Russia, where he has been granted temporary asylum.
"The majority of the stolen reports are likely to discuss political, economic and military intelligence gleaned by Australian agencies, especially the Australian Signals Directorate in the Asia-Pacific region," the front page report said, without citing sources.
The broadsheet added that it understood a massive audit is under way to assess what was in the files, although the volume of material means it is a slow, painstaking process.
Over the past six months, Snowden's leaks have laid bare the scale of spying by the United States and other countries, often on their own allies. In an interview with the newspaper, Attorney-General George Brandis said that they were massively damaging.
"The Snowden revelations are the most serious setback for Western intelligence since the Second World War. Given that most of the sophistication and the structure of Western intelligence-gathering was developed since the Second World War, it would not be an exaggeration to say it is the most serious ever," he said.
Brandis said the disclosures were worse than those of Wikileaks or Cold War British spies Kim Philby, Guy Burgess and Donald Maclean due to their sheer breadth.
"The extent of it is vast, we are talking about huge numbers of files which Snowden has put into the public domain," he said.
Reports based on Snowden leaks last month showed Australian spies tried to tap the phones of Indonesian President Susilo Bambang Yudhoyono, his wife and his inner circle in 2009, triggering an embarrassing row.
Jakarta reacted furiously, ending cooperation on military exercises and in the key area of people-smuggling while recalling its ambassador from Canberra.
Documents already released have proved a major headache for Canberra, sparking its worst diplomatic crisis in years with neighbour Indonesia amid warnings that more revelations appear likely.