The Australian Greens and several independent MPs are lobbying the government to secure a commitment from the Australian Bureau of Statistics that it will not fine anyone who doesn't properly complete this year's bungled Census.

Independents Nick Xenophon and Jacquie Lambie have co-signed the Greens' motion, which is scheduled to be introduced into parliament when the Senate next sits on September 12.

The motion calls on the government to "direct the Australian Bureau of Statistics to issue a statement declaring that no Australians will be fined for failing to complete the Census".

The ABS has the power to direct people to complete the form, and to issue penalties of up to $180 per day for continued failure to fill out the national survey.

Providing false or misleading information could see an individual fined up to $1800.

The MPs argued the technical failure of the online Census form on the night of the national survey and subsequent days prevented "thousands" of people from completing it.

They said the ABS' attempts to deal with the IT problems "added to confusion and impacted public confidence in the Census process".

In addition, some Australians purposely chose not to properly complete the Census due to privacy concerns, after the ABS this year decided for the first time to retain citizens' names and addresses and turn them into linkage keys to connect with other data sets.

It is unclear whether the opposition Labor Party or the government will lend their support to the motion and give it the numbers to pass.

The same MPs were yesterday successful in their efforts to refer the Census IT and privacy problems to the parliamentary economics reference committee for a full investigation, thanks to the support of Labor.

Update 12/9/16: The motion was defeated after Labor sided with the Coalition.