The census website has been restored more than 40 hours after being taken down due to cyber attacks and a hardware failure.
The online form became available on Thursday afternoon, after the Australian Signals Directorate gave a written all-clear to the Australian Bureau of Statistics.
ABS boss David Kalisch, who again apologised for any inconvenience, told reporters he had been assured the system was "safe and secure" and Australians' data would continue to be protected.
"We would request Australians continue to show their support and complete the census fully and accurately," he said in Canberra.
The ASD has told the Australian Privacy Commissioner Timothy Pilgrim that the denial-of-service (DOS) attacks on the site had not accessed or extracted any personal information.
"On the information provided to me by ASD, I am satisfied that personal information was not inappropriately accessed, lost or mishandled," Mr Pilgrim said in a statement.
Mr Pilgrim said the ABS decision to shut down the census site was "a pro-privacy precaution".
Earlier, an angry Malcolm Turnbull signalled heads will roll after revealing measures were not in place to repel DOS attacks that left the census website in meltdown.
A clearly frustrated prime minister admitted there were "serious failures" with the national survey, which was conducted on an opt-out online basis for the first time by the ABS.
"It shouldn't have happened. I am not happy about it. None of us are," he told reporters in Canberra on Thursday.
DOS attacks were inevitably going to happen to the census website, especially given its high profile, he said.
"A denial-of-service attack is as predictable as the rain will fall one day, or the sun will come up," Mr Turnbull said.
"Measures that ought to have been in place to prevent these denial-of-service attacks interfering with access to the website were not put in place. That is a fact."
The failure of prevention measures was compounded by hardware problems, he said - pointing to "big issues" for the ABS and IT company IBM, which was contracted to carry out the census.
Mr Turnbull foreshadowed "very serious consequences", following a review to be undertaken by the government's cyber-security adviser Alastair MacGibbon.
"Which heads roll where and when will be determined once the review is complete," he said.
Opposition Leader Bill Shorten criticised Mr Turnbull for failing to take responsibility for the shambles, especially given he changed the minister responsible for the census three weeks out.
"His failure to take responsibility is a failure of leadership," he told reporters in Melbourne.
Mr Shorten called for an independent Senate inquiry into what went wrong and why.
With 2.3 million forms already completed online and 3.7 million forms with households, another four million filled-out forms will be needed to ensure a quality end product.
It is understood ABS and computer provider IBM knocked back a proposal for extra defences to fend off a cyber attack.
Patrick Gray, an experienced journalist who hosts the popular Risky Business podcast, said the upstream provider NextGen Networks had offered DOS protection services for the census.
But the ABS and IBM said they did not need it.
However, when the initial DOS attack came on Tuesday morning, NextGen was called in to geoblock traffic coming from outside Australia.
NextGen declined to comment when contacted by AAP.
