Covid-19 response minister Chris Hipkins said the variant "changes the game considerably" and makes existing protections "look less adequate".
It comes as the country announced a further 21 confirmed cases in the latest outbreak of the virus.
New Zealand had quashed earlier Covid outbreaks with rapid, strict lockdowns.
The country was praised for its efforts, which effectively stopped the spread of the virus. Prime Minister Jacinda Ardern has repeatedly referred to New Zealand as "our team of five million".
According to Johns Hopkins University data, there have been 3,016 total confirmed cases in the country, and 26 reported deaths.
But authorities recently announced a snap lockdown after one man tested positive in Auckland with the Delta variant.
There are now 72 active cases. Seven schools in the city have reported positive cases among students, and the country has also announced six infections in the capital, Wellington.
Officials are now warning that they will probably extend the Auckland lockdown, which is set to expire on Tuesday.