Prime Minister Malcolm Turnbull has unloaded on the Australian Bureau of Statistics (ABS) over its handling of the botched census, but says possible sackings will not come until after a full investigation.

Key points: The site has gone back online, more than two days after it was disabled

The site has gone back online, more than two days after it was disabled "This has been a failure of the ABS," the PM says

"This has been a failure of the ABS," the PM says Turnbull's special cyber security advisor says more attacks expected

The census was now back online on Thursday, almost two days after it was shut down following a denial of service cyber attack.

Mr Turnbull fronted press gallery reporters in Canberra, expressing his unhappiness over events which he said had "inconvenienced millions of Australians" after the ABS shut down the census website on census night in response to what it called a series of denial of service cyber attacks.

The census collection process was paralysed for days, leading the Labor Party to describe it as one of the biggest shambles in the history of the Australian government.

"Which heads roll, where and when, will be determined once the review is complete," Mr Turnbull said.

"I made it very, very clear that what we needed to do was be absolutely straight and frank with the Australian people.

"This has been a failure of the ABS."

The head of the Australian Bureau of Statistics, David Kalisch, delivered another mea culpa, in the form of a statement to reporters in Canberra this afternoon.

"I would again apologise for the inconvenience suffered by many Australians," he said.

He said the website was only put back online after a written assurance from the Australian Signals Directorate that the system was safe and secure.

He did not take any questions from reporters.

Sorry, this video has expired ABS Chief Statistician David Kalisch says the online census form has re-opened

Labor has criticised the Prime Minister for distancing his Government from blame, with Opposition Leader Bill Shorten describing the unfolding events as "one of the biggest shambles in government".

Mr Turnbull said denial of service attacks were "predictable" and the ABS-contracted service provider IBM should have been prepared.

"Part of the job of the service provider, in this case IBM, was to ensure that there were measures to repel denial of service attacks," he said.

"The fact is the measures that were put in place were inadequate."

A spokesperson for IBM said the company "genuinely regretted the inconvenience" that occurred, and that it remained committed to maintaining privacy and security of personal information.

"IBM's priority over the last two days was to work with the ABS to restore the census site. We are committed to our role in the delivery of this project," the spokesperson said.

"The Australian Signals Directorate has confirmed no data was compromised. Our cyber-security experts are partnering with national intelligence agencies to ensure the ongoing integrity of the site."

PM says source of attacks will be investigated

Mr Turnbull said that while ministers held overall responsibility for their portfolios, the ABS had ultimately been in charge of the census collection process.

"Right now, my objective as PM is to ensure that the site is back up, it should be restored today, that is the advice I have as of a little while ago."

The Prime Minister said that while the attacks appeared to be coming from the United States, that did not confirm that the US was the source of the disruptions.

"It is relatively straightforward to be able to route traffic using virtual private networks and other techniques through the US," he said.

"That will be investigated."

Sorry, this video has expired Cyber security expert says ABS could not have foreseen confluence of events

Earlier the PM's special cyber security advisor Alastair MacGibbon said more attacks were expected when the site goes back online.

Mr MacGibbon said there were no absolutes in cyber security, but "everything conceivably possible able to be done will be done to protect" the site.

"Every effort is being made," he said.

Both Mr Shorten and crossbench senator Nick Xenophon have called for a Senate inquiry into the handling of this year's census.

Senator Xenophon told the ABC that he had spoken with Mr Shorten and had begun working on the terms of reference.

He said "heads will have to roll" if an inquiry finds that the site was simply overwhelmed by users rather than being attacked — a scenario which has been put forward by some cyber security experts.

Only 2 million households able to complete census

In a statement issued on Wednesday night, the ABS said it was working with the Australian Signals Directorate and its partners, and apologised that the online form was still unavailable.

Only 2 million households were able to complete their census forms online before the site crashed.

The ABS says people have until September 23 to fill in the online census and that those unable to do so will not be given a fine.

The bungled survey, dubbed #CensusFail on social media, drew criticism from many in the privacy sector, including the former NSW deputy privacy commissioner, who said the results should be scrapped.

But the minister responsible for the census, Michael McCormack, dismissed privacy concerns and insisted the website was not "attacked", despite confirming the site was shut down after repeated denial of service attempts.

Sorry, this video has expired Census fail: Was it a hack, an attack or something else?

When pressed on his language, Mr McCormack said he felt that "by saying attacked, it looks as though and it seems as though and it is so that information was then gained".

Later on Wednesday, it appeared as though the minister himself had been the subject of a cyber attack, when an errant link labelled "gay sex" was spotted on his official website.

It hyperlinked to what appeared to be a Polish finance company's website.