The website for the census, which was conducted online by the Australian Bureau of Statistics for the first time, was shut down on Tuesday night after a series of cyber attacks and Mr Turnbull says the threat should have been addressed.
"This has clearly been a failure on the part of the ABS. Measures that ought to have been in place ... were not," Mr Turnbull told Sydney radio 2GB.
Millions of Australians are still waiting to fill out their Census forms after the Australian Bureau of Statistics website crashed on Tuesday night and remained inaccessible on Wednesday.
The ABS has not yet confirmed when the website will be back up and running for the 20 million or more people who have yet to complete the compulsory survey.
The ABS was in damage control on Wednesday after its first online Census trial ended in disaster when the website crashed and then became unavailable, with conflicting reports coming from the ABS and the federal government about exactly what went wrong.
While the ABS cited foreign hackers as being responsible for the crash, Census minister Michael McCormack contradicted this report, claiming the crash was not due to an attack.
"This was not an attack, nor was it a hack," Mr McCormack told reporters on Wednesday, despite ABS Chief Statistician David Kalisch describing the events leading up the shutdown as "malicious" and "an attack" earlier on Wednesday.
However, the ABS has confirmed no data has been compromised or lost.
Just after 7.30pm on Tuesday, a number of events simultaneously led to the crash, according to an ABS media statement.
These included a large increase in online traffic, a router becoming overloaded, leading to a hardware failure, a fourth "denial of service" attempt, meaning a user was denied access to the website and a false alarm in some system monitoring information.
"Had these events occurred in isolation, the online system would have been maintained," the statement read.
More than two million forms had been successfully submitted and stored before the website crashed, according to the ABS.
Despite numerous attempts to contact the ABS for further information on Wednesday night, AAP did not receive a response.
