However, the West Australian said the party would prefer if the federal government and the Australian Bureau of Statistics acknowledged that problems with the census had eroded Australians' trust in the five-yearly population count and took steps to ensure that fines were not levied on citizens for taking steps to guard their privacy.
The census was supposed to be held on 9 August with 60% of the population expected to complete it online. However the ABS took the site offline at 7.30pm, claiming that it had done so due to repeated distributed denial of service attacks.
More than a week later, just half of the Australian households have completed the census, as per information from the ABS on Thursday.
Standing firm: Scott Ludlam. Photo: courtesy The Greens.
Ludlam, along with his Greens colleagues Sarah Hanson-Young, Lee Rhiannon, Janet Young and Larissa Waters, had said on the day of the census that they would be withholding their names when filling in their census forms.
South Australian Senator Nick Xenophon, who heads his own party, and Tasmanian Jacqui Lambie joined the five Greens, saying they were not convinced the census did not present a security risk.
Asked on Thursday whether he had spoken to other MPs in connection with his census day statement, Ludlam responded: "We'd much prefer that the government and the ABS acknowledge that the multiple problems with the census eroded Australians' trust in the process, and take the necessary steps to assure people that they will not be penalised for taking steps to protect their own privacy.
"The changes to the census should never have proceeded without thorough, transparent independent assessment."
He added: "The ABS should abandon the linkage key process for this census. Perhaps after civil society advocates and experts have closely examined the changes, Australians will feel more reassured. More likely, this independent assessment will find that the linkage key poses a significant threat to privacy and changes the character of the census in ways that make participation less likely."
A proposal to link names was considered for the 2006 census but dropped after a privacy impact report, by privacy expert Nigel Waters, advised strongly against it.