Ten new cases of Covid-19 have emerged since Friday, all in managed isolation centres.
In an update shortly after 1pm on Sunday, the Ministry of Health said one of these cases was classified as historical, and not infectious.
Eight of the new cases are in Auckland, and one in Christchurch.
The historical case involved a person who travelled from Pakistan via the UAE on September 5. They completed managed isolation and returned two negative test results in September but were recently retested as a pre-travel requirement. That test returned a weak positive result, indicative of historical infection.
Of the new potentially infectious cases, two people arrived from South Africa via the UAE on Thursday. Both were tested on their first day in New Zealand.
A person from the United Kingdom who also travelled through the UAE and arrived on Thursday has tested positive too.
One of the people who tested positive was from an undetermined country and arrived last Tuesday.
Others who tested positive came from Japan, the UK, the United States and the UAE.
"Four cases have now recovered, bringing the total number of active cases in New Zealand to 82," a Ministry of Health spokesperson said.
Since the pandemic erupted, New Zealand has recorded a total of 1900 cases.
Meanwhile, the first travellers from Britain and the US under new pre-departure testing rules have started arriving in New Zealand.
New Zealand Customs reported very high levels of compliance with the new rules, the Ministry of Health said.
Since 11.59 pm on Friday, travellers from the United States and UK have had to produce a negative Covid-19 result or signed medical exemption on arrival in New Zealand.
On top of this, travellers from these two countries must get a Covid-19 test within 24 hours of arriving into managed isolation.
These new arrivals have to stay in their rooms until a negative test result is returned.
Pre-departure testing will soon include all countries and overseas territories apart from Australia, Antarctica and some Pacific Island nations.
Health authorities hoped the new testing rules would better protect New Zealand from Covid-19, including from new and emerging mutant strains of the virus.