The website is yet to be restored, with millions of Australians unable to lodge their information because of the closure.
Malcolm Turnbull says measures were not in place to repel the sort of attacks which threatened the census website.
He says there were serious failures with the conduct of the Australia Bureau of Statistics national survey, which was predicted to have many more online respondents this time than in the last census, in 2011, so was being conducted primarily over the internet.
Mr Turnbull says the failure of prevention measures was compounded by hardware problems.
He has refused to say who will be made accountable because of the fiasco but has foreshadowed very serious consequences.
And he's blaming the Bureau of Statistics and IBM for being unprepared for the cyber attacks.
"Which heads roll, where and when will be determined once the review is complete. Right now my objective, as Prime Minister, is to ensure that the site is back up. It should be restored - that is the advice I have as of a little while ago. And that when it is restored it is - the protections that ought to have been in place are in place. But there has clearly been a failure."
Minister for Defence Industry Christopher Pyne says the Australian Signals Directorate is looking into just what happened, and he can't guarantee the public will ever be told the exact details.
Mr Pyne says the government is taking the issue very seriously indeed which is why the intelligence agency is looking into the matter.
"As with all these matters of course, some of them can have highly secure, highly classified outcomes, and the capability of the ASD is not necessarily one where we want everyone to know exactly what we are able to do. So it has a certain level of secrecy and discretion that is the highest in government. So I can't commit to releasing everything the ASD finds out but I can assure the public that the government will do everything it can to find out why this happened, to ensure it doesn't happen again."
Mr Pyne has promised to release whatever information he can.
Opposition Leader Bill Shorten says those assurances are not good enough, and Mr Turnbull should not be blaming public servants for the fiasco.
"Malcolm Turnbull is always talking about blaming someone else. When Malcolm Turnbull gets paid every week, what does he think this pay is for? It's his job to make sure that everyone else in the government does their job properly. Now he is just lashing out the one thing we have learned about Malcolm Turnbull in his year as PM is when there is a problem he will be sure to blame someone else. Malcolm Turnbull never takes responsibility for mistakes that happen under his leadership, that is not good enough."
Meanwhile the man who will run the investigation into the attacks says all the speculation about security of the online survey made it an easy target.
Malcolm Turnbull's cyber-security adviser Alistair MacGibbon says the census became a big target after talk about security in the lead-up to Tuesday night.
