Prime Minister Malcolm Turnbull has reassured Australians their data is safe after the census was shut down due to cyber attacks.

The Australian Bureau of Statistics took down the census website in "an abundance of caution" on Tuesday night, Mr Turnbull told reporters in Sydney.

The site would be restored as soon as intelligence agency Australian Signals Directorate and the ABS and its contractor IBM were satisfied it was safe to do so, he said.

"The site has not been hacked, it has not been interfered with, their data is safe."

Mr Turnbull said his cyber security adviser Alastair MacGibbon would lead a "very thorough review" into what happened.

Treasurer Scott Morrison said the ABS had an unblemished record when it came to security of census data and had taken every step on Tuesday to protect that record.

"The issue the ABS has been criticised for is being over-cautious last night," Mr Morrison said.

"They chose to place people's data security and any possible, possible compromise to that as being more important than convenience last night."