Statistics New Zealand is in dispute with a parliamentary committee after not releasing information about the poor response to last year's Census.
The Census used an online model for the first time and it is estimated more than 400,000 people did not take part.
The Government Administration Select Committee has demanded details of the response to last year's Census, of which results would normally have been released by now.
The committee has demanded answers by Wednesday.
Chief statistician Liz McPherson said on Wednesday, "now is not the appropriate time to release information about the full and partial responses to the 2018 Census".
In a statement, Ms MacPherson said she would release the information in an announcement at the end of this month.
"Without the appropriate context, these individual numbers would be open to misinterpretation," she said.
The National Party's statistics spokesperson, Dr Jian Yang, said parliament needed the partial response rate "now" in order to understand the quality of 2018 Census data.
"And secondly, we want to know if the further delay of Census 2018 data release is because of not only the low response rate but also a high partial response rate."
He said not having the information made it difficult to hold the government to account.
He said the electoral commission would struggle to redraw electorate boundaries without the Census data and the government might have to use "very old" or "very unreliable" data to plan for this year's Budget.
"So this 2018 Census has huge implications for the function of various government agencies and it won't serve the interests of New Zealanders very well.
"Had the chief statistician given us the information, the issue might have been resolved."
The fact she had not had "escalated" the situation meant she would face committing contempt of parliament if she did not meet Wednesday's deadline.
A review of the management of the Census is due to report in July.