"It was an attack," chief statistician David Kalisch told ABC radio on Wednesday.
"It was quite clear it was malicious."
The ABS is now working with the Australian Signals Directorate to determine the source of the attack.
Mr Kalisch said so far it had been very difficult to work out where it came from.
In the past Australian government websites have been attacked by Chinese hackers.
A number of digital assaults on the census website began during the day on Tuesday and were repelled.
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.
"I can certainly reassure Australians the data they provided is safe," he said.
The ABS released a statement around 11.30pm on Tuesday advising the websites was unavailable.
It's reassured Australians they won't be fined for not completing the census on Tuesday.
Mr Kalisch said he expected the site would be back on line around 9am on Wednesday.
Mr Kalisch and the minister in charge of the Census, Michael McCormack, will hold a press conference in Canberra later on Wednesday.
Labor calls for census minister to resign
Labor wants the minister responsible for the botched census, Michael McCormack, to resign and believes a re-run is not out of the question.
Shadow assistant treasurer Andrew Leigh is furious the government failed to properly explain its decision to take the national survey online, where it was then subject to foreign cyber attacks on Tuesday night.
"If you can't get the census right how can you govern the country," he told ABC radio on Wednesday.
Dr Leigh criticised the coalition for leaving the position of chief statistician vacant for a year and feared it would now blame the bureaucrats.
"What I'm concerned about is that the government is going to pass the buck," he said.
Dr Leigh urged people to hop online as soon as the website is working again.
