The government does not know how many foreigners have come into New Zealand under the essential worker exemption and says it would "not be a great use of officials' time" to find out.

While the border is closed to all but NZ citizens and residents, employers can apply to bring in workers from overseas if they are deemed "critical".

A media statement issued on 12 June stated that 237 people had been granted an essential worker exemption and invited to apply for a visa.

But in response to a written question from the Opposition, Immigration Minister Iain Lees-Galloway declined to say how many of those people had since arrived.

"I am advised that to provide the number of those who then entered New Zealand would require substantial collation and would not be in the public interest," the response said.

Speaking to RNZ, Lees-Galloway doubled-down on the position, saying officials were too busy to find the "precise number".

"It actually means manually trawling through databases and looking for each individual arrival across the border," he said.

"That would not be a great use of officials' time when we've got a pandemic to face."

National's immigration spokesperson Stuart Smith told RNZ that was "unbelievable" given it was only a few hundred people.

"That's not a lot of data," he said. "You could go through with a calculator and work it out yourself. I don't think it's that difficult."

Smith said the response smacked of arrogance and made him question whether the information was even being collected.

"What are they trying to hide here?" Smith said.

"They're not keeping records on things. They don't know who's coming across the border... They aren't managing the border at all."

A spokesperson for Immigration NZ said there was sometimes a delay between people being granted an exemption and them then applying for a visa and making travel arrangements.

She said, as such, the information requested was not "easily reportable".

"We would have to look at each of the individuals to see whether they have put their application for a visa in, whether that has been approved and then also whether they have travelled to New Zealand yet."

New criteria for the essential worker exemption was issued on 12 June, but no requests have been approved since that date.