National is accusing Statistics Minister James Shaw of "swanning around the Pacific" while his department grapples with census problems.
Former statistics minister Scott Simpson says it's "unbelievable" Mr Shaw is out the country during the most important interaction his department has with the public.
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"He has chosen to be swanning around the Pacific on a junket while his officials at Statistics NZ are left to carry the can," he said.
"There are real concerns around New Zealanders not receiving their code letters, some are struggling with online access and many are reporting a lack of response to queries and calls for help."
Mr Shaw, in his capacity as Climate Change Minister, is with Prime Minister Jacinda Ardern on her Pacific Mission which runs for the rest of this week.
The Statistics Department has given assurances it is on top of the issues around the census.
It says letters will soon be on the way to households which haven't received their online access number, and people who ask for paper forms will receive them.
Although Tuesday is Census Day, the forms can be completed before or after it so long as they show the state of households on March 6.
The department's general manager, Denise McGregor, says codes have been delivered to 96 percent of the country.
After Tuesday, field teams will be out following up on households that haven't responded.
By midnight Monday 1.74 million forms had been filled out online, a figure the department says is "promising".