Health Minister Chris Hipkins says people at managed isolation facilities are not tested for Covid-19 every day but there is a system of regular testing.
It comes after a maintenance worker at the managed isolation facility at the Rydges Hotel in Auckland tested positive for the virus.
The man, who had a cough but still went to work for two days, is not linked to the Auckland August cluster.
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Earlier today, Managed Isolation and Quarantine Minister Megan Woods said the man passed his health checks at the time, including a temperature check.
Speaking on Newstalk ZB's Heather Du Plessis-Allan Drive, Health Minister Chris Hipkins said it was standard procedure when asked why he wasn't swab tested.
"We don't test people every single day, we do have a system of regular testing, there was regular testing at the hotel where he was working at the week before," he said.
"He was picked up in a regular sweep of testing the following week. We do have to monitor people in between times but we don't test them every day."
The man attributed the cough to a preexisting condition, which Hipkins said can explain why some people have "a cough or sniffle".
The worker tested positive on Sunday, August 16, but showed symptoms from August 11.
Elsewhere, Hipkins said it would be unnecessary to test all border staff with a swab each week.
Temperature tests are given each day when people arrive for work but if they do have symptoms for Covid-19, they are tested straight away.
The Health Minister will later this week release a new order outlining the new testing regime, which will not require all border staff to be tested each week.
"People working at Jet Park, for example, our expectation is that they will be tested weekly because they're working in a hot zone with people who have Covid-19," he said.
"Someone who is moving trolleys around in the car park at the airport would be lower risk and the testing might not be as frequent there.
"There are thousands of people who work at the port and the airport and we don't need to test them every week."
The current sweep of testing, following the Auckland August cluster, is covering all people working at the border.
However, the order Hipkins says he will sign this week will only be mandatory in circumstances where people are considered of higher risk.
"People working on the airside of the border coming into contact with people coming on and off planes, they're at higher risk so there'll be a stringent, regular testing regime for them," he said.
"Those working on the New Zealand side of the border, who aren't coming into contact with people coming off planes, the risk there is lower so the testing doesn't need to be as frequent."
"Anyone showing symptoms, of course, will get an immediate test."
Hipkins assured Du Plessis-Allan the test would be a swab test.
Asked whether all aircrew are being tested coming into the country, Hipkins said they were testing those from "higher risk" countries.
The order being released later this week will provide more information about how and what aircrew will be tested.
Hipkins says there is "a lot of complexity" around the testing and that he was working with airlines to sort out logistical issues.
"We've got to understand the risk, all of the potential areas where things can go wrong and mitigating them," he said.