Gluckman's warning follows the Teaching Council of Aotearoa New Zealand's call for the closure of schools as the country's case toll continues to climb.

Cabinet is meeting on Monday morning to discuss the next steps to fighting the novel coronavirus, which has infected 66 people nationwide.

Prime Minister Jacinda Ardern will address the media at 1:30pm with the latest updates on the outbreak.

New Zealand is currently sitting at alert level two after the four-stage alert system was revealed by Ardern on Saturday.

Alert level one: Prepare

This level applies when COVID-19 is present in New Zealand but contained. Before Saturday, New Zealand was at this phase due to the risk of importing the illness and sporadic cases. There were a few cases of transmission within households. In response, some border measures were introduced, contact tracing began, self-isolation for the infected and their close contacts was required and limits were put on mass gatherings.

The public was encouraged to consider limiting their exposure to others through physical distancing and staying home when feeling unwell. Key messages of preventation began to be frequently communicated.

Alert level two: Reduce - New Zealand's current level

New Zealand moved to this level of Saturday after authorities deemed the likelihood of new cases as high. There has been an increase in imported cases and cases transmitted within households. This suggests that COVID-19 is contained, but the risk of community transmission is growing. Currently, there is no confirmation of community transmission in New Zealand - however, two cases don't have clear links to overseas travel and investigations remain underway.

Under this level, border measures have been increased and more restrictions have been put on mass gatherings. Authorities are now calling for greater physical distancing on public transport, limiting non-essential travel around the country, new ways of working - such as remote working - businesses activating their continuity plans and vulnerable people, including those over 70, to stay at home.

Alert level three: Restrict

Level three would come into effect if authorities believed there was a heightened risk of the illness no longer being contained. This could mean that community transmission is evident or multiple clusters of COVID-19 have broken out. Those regions or centres with clear clusters or community transmission could have their travel limited, public venues and affected educational institutes closed, mass gatherings banned and alternative ways of working required with some non-essential businesses closed.

Changes would also be introduced within the health system. For example, primary care consultations would no longer be face-to-face, while elective services and procedures would be deferred to allow for healthcare staff to be freed up.

Alert level four: Eliminate

This is the top-level and would be activated if it is "likely" COVID-19 is not contained nationally or at a local level. There would have to be intensive and sustained transmission with widespread outbreaks. Under this level, people would need to stay at home, all educational facilities and non-essential businesses closed, supplies would be rationed, facilities would be requisitioned, travel would be severely limited and all healthcare services would be reprioritised.