The company which made the claim, Resecurity, said the attack was part of a wave which had targeted the Five Eyes intelligence alliance: the US, the UK, Canada, Australia and New Zealand.
His claim was contested by an American security professional, Joseph Carson of security outfit Thycotic, on Wednesday.
Resecurity president Charles Yoo told The Wall Street Journal that the Mabna Institute was linked to Iran's Revolutionary Guard.
But the Sydney Morning Herald, citing "top-level sources", said China, not Iran, was behind the attack. These sources termed the Mabna theory an unlikely one, adding that China remained the main suspect.
As proof of his claim, Yoo showed the WSJ a database of 7354 records which had phone numbers and email addresses for Australian MPs and parliamentary staffers. It also included contact details for staff and ministerial advisers of most parties.
However, he did not say from where he had obtained the material.
iTWire sought to obtain more detail from Resecurity as the company had not issued a formal statement about its claims. A spokesperson said the company would issue comment soon, but nothing was received by the time of publication.
Comment was also sought from the Australian Cyber Security Centre about the competing claims of attribution. The ACSC said it would respond but had not done so at the time of publication.
Update, 23 February: An Australian Cyber Security Centre spokesperson said in response to a query: "Our cyber experts believe that a sophisticated state actor is responsible for this malicious activity.
"It would be too early to speculate on the specific offender – our immediate focus has been on securing the networks, protecting victims and conducting ongoing investigations.
"Proper and accurate attribution of a cyber incident takes time and any attribution would be done in a measured fashion.
"The public can rest assured that our security and intelligence agencies have identified the malicious activity and are responding appropriately."