The Director-General of Health has no doubt the cases of community transmission of Covid-19 are on the rise.
It's not yet known how New Zealand's first Covid-19-related fatality caught the virus.
The woman in her 70s died in Grey Base Hospital yesterday morning.
Ashley Bloomfield was asked how many of the 514 cases to date have been community transmission.
"I don't have the exact figure and of the new cases in the last day or two, many of those are still being followed up and investigated.
"The number associated with community transmission will be increasing, I have no doubt about that, and particularly because we are seeing those small number of clusters around the place," Dr Bloomfield said.
"Most (of the cases in NZ) are still related to people who have travelled back or who had close contacts of those who did so it will take a while for that shift to happen, but probably in another week or so we will start to see more of our cases, it's hard to know when the balance will shift though," he told Morning Report.
Some of the modelling on which the government has relied on for its response will be released in the next day or so; the prime minister said the rest was already publicly available.
Meanwhile, the death of an elderly woman in Greymouth from Covid-19 has led to a change in the precautions medical staff are taking to protect themselves.
"This person came in with classic flu symptoms, there wasn't any reason to suspect Covid-19 because of the history initially, so appropriate precautions were taken as if this person had influenza, so masks and gloves and other PPE (Personal Protective Equipment) were used, just not the visors," Dr Bloomfield said.
"What we are recommending now is that anyone who is coming in, either to primary care practice or to an emergency department with symptoms of a respiratory illness like that, what we call a lower respiratory tract infection like a pneumonia or bronchitis, is treated as if they've got Covid-19 until proven otherwise so that has led to a shift in practice."
Dr Bloomfield says it is still not clear how the woman who died caught the virus.
Numbers 'expected' to dip - researcher
Auckland University physics professor Shaun Hendy is leading researchers at modelling the coronavirus.
He says the total number of cases so far has been expected, due to the high number of people returning from overseas.
"Of course when the travel restrictions came on about two weeks ago we had a big spike of people returning and those people are now passing through that incubation period," he told Morning Report.
"We're actually expecting numbers of people infected overseas to start dropping in those daily updates, and then we go into that period where we'll be looking at the pre-lockdown infections.
"We don't quite know what those will look like, then perhaps next week and the week after we'll start to see the effects of the lockdown, people who might've been infected during lockdown and we'll start to get a handle on how the lockdown is working and then by week three we'll have a little bit of an insight into how well the lockdown has worked."
Hendy said people should also be careful comparing raw numbers to other countries.
"How well the lockdown has worked will have a big impact, the lockdown will definitely be slowing things down, if you look at those clusters that have been talked about at the high school, in Matamata, those clusters are quite large and it just shows the importance of sticking to your bubble.
"If you're in your bubble and that consists of your family, those sort of clusters are not going to be occurring now and that will eventually start to pull down our numbers."