StatsNZ has been giving away free Warriors tickets and food vouchers to try to coax more people into sending back their Census forms, with the deadline looming.
It could not say how much it had spent on the incentives, but so far the response fell short of its expectations.
Its target is 90 percent of the population, but so far only about 86 percent of people had taken part, or 4.4 million people.
The National Party said Statistic Minister Deborah Russell needed to from up over the failure after staking her reputation on reaching the target.
Deputy chief executive of census and collections Simon Mason told Checkpoint late replies were vital to the final count, and they were still on track to reach 90 percent.
Census day was 7 March, and everyone in the country on that day was legally required to fill the form out, with the main cut off date this Wednesday, 3 May.
Census collectors would still be out working in communities to collect the forms and help people fill them out until this Wednesday. However, those in areas that had been impacted by Cyclone Gabrielle had until 1 June.
Anyone who refused or supplied false information could be prosecuted, and fines up to $2000 could be imposed by the court.
Mason said he expected there would be prosecutions.
There had been increased distrust about filling out the forms this year, he said.
"It's not been without it's challenges ... that probably follows the Covid response and vaccinations and other things - trying to get people to engage with government is quite a hard thing to do, but a very important thing to do.
However, the reduction in response rates was an international trend over many years which New Zealand was not an exception to, and the reduction had only increased "slightly" during the Covid-19 period, Mason said.
"There are many reasons why people don't want to give us their information. Some of them are a little bit worried about privacy and what we'll do with the information.
"And of course we don't share people's personal information with anybody - we only publish aggregated statistics about their general well-being, not about individuals directly. And the information is protected by law - so sometimes that message just doesn't make its way through."
Census workers had given out 2000 Warriors tickets, and had 2000 food vouchers to give out, which had been "a really successful part of our engagement", Mason said. He had heard directly from many of those who had taken part that they had never before filled out a census form until those events.
Showing up and holding events was vital for reaching those who don't listen to or read media, news or social media: "And there are people out there that don't do either of those things," he said.
"Homeless people are just one example of that, but there are others that just don't engage with media or other social channels, so going to where the people are is very important to Census - at the end of the day Census is about people."