"It was an attack, and we believe from overseas," chief statistician David Kalisch told ABC radio on Wednesday.

"It was quite clear it was malicious."

The site was targeted by four denial of service (DoS) attacks, he told the ABC.

"The first three (attacks) caused minor disruption, but more than two million forms were successfully submitted and safely stored.

"After the fourth attack, which took place just after 7.30pm (AEST), the ABS took the precaution of closing down the system to ensure the integrity of the data," Mr Kalisch said.

"I can certainly reassure Australians the data they provided is safe," he said.

Australian Signals Directorate - an intelligence agency within the Australian Department of Defence - are investigating, but they indicated it would be very difficult to find the source of the attack, Mr Kalisch said. 

Mr Kalisch said so far it had been very difficult to work out where it came from.

Some IT and cybersecurity professionals speculated that a DDoS attack was to blame, in which hackers attempt to crash a system by flooding it use bots, or Trojan, accounts. 

But a handful of Twitter users pointed to digital attack maps that showed no DDoS activity in Australia on Tuesday. 

In the past Australian government websites have been attacked by Chinese hackers. 

As an estimated 16 million people logged on to the census website on Tuesday night, they were met with error messages and told the system was "overloaded" before the website crashed.

But the frequency increased as the evening neared and many Australians trying to reach the census site after 7pm couldn't connect.

It was at this point the ABS said it began the process of shutting down the site.

Mr Kalisch said he believed the details of people - including Prime Minister Malcolm Turnbull - who had managed to successfully access the site were secure.

"Steps have been taken during the night to remedy these issues and I can certainly reassure Australians that the data they provided is safe," he said.

The ABS released a statement about 11.30pm on Tuesday advising the website was unavailable.

The ABS had dismissed suggestions an overload could cause the system to crash earlier in the day.

But the troubles began about 5pm on Tuesday, when people trying to access the form were stopped by messages including a "code 31" error, which said the request "could not be completed because a problem was encountered".

Late on Tuesday night, the Bureau conceded the census would remain down at least overnight.

"ABS & Census website are unavailable. The Service won't be restores tonight. We will update you in AM. We apologise for the inconvenience," the Census Australia Twitter account tweeted just before 11pm. 

Mr Kalisch said he expected the site would be back on line about 9am on Wednesday.

The minister in charge of the Census, Assistant Treasurer Michael McCormack, will hold a press conference in Canberra on Wednesday morning.

Australians who failed to fill out the census because of the hours-long website outage will not be fined, and have until September 23 to complete the survey, the federal government says.

Labor is demanding the Minister responsible for managing the census,Mr McCormack resign over the embarrassing website crash, which the Australian Bureau of Statistics said hours earlier could not happen.

The census was plagued by a growing boycott over fears of potentialsecurity and privacy breaches. 

The Australian Bureau of Statistics controversially switched to an opt-out online format this year and moved to store your personal data for four years rather than 18 months.

ensus was delivered by technology company IBM using its Australian SoftLayer cloud. Figures from the Australian Government's procurement agency AusTender show IBM was paid $9,606,725 in 2014 to design, develop and implement the "eCensus".

Although the names will be destroyed after those four years, the ABS created linkage keys which link names to other data they collect which will be kept indefinitely. The ABS says, however, that staff cannot get back to the name once it is destroyed from the other data via the key.