Prime Minister Jacinda Ardern says she expects further tightening up of rules for returning travellers in the next few days.
She told Morning Report quarantining all New Zealanders returning from overseas would not have been possible.
"The sheer magnitude of New Zealanders who travel meant that would not have been possible, nor in a way that I believe we could've guaranteed that we didn't have an example of the Diamond Princess on soil where you have a spread.
"We're looking at alternative ways to get that extra layer of guarantee, I'm not in a position to talk about that yet but that will be my focus in the next 24 hours.
"I want further tightening up on returning travellers."
Those measures could be expected in the next few days, she said.
However, Ardern said there was nothing to suggest that confirmed cases in self-isolation were not adhering to rules because all acknowledge the seriousness of it.
She also reiterated her message from Monday - she expects things would get worse before the effects of the lockdown would come into play and cases would reduce.
"There is a lag time with Covid-19 so the time from which someone picks it up to the time they get symptoms and get tested.
"So I expect over the next two weeks, cases will go up, particularly as we've had New Zealanders come home or New Zealanders who have travelled, and they do represent the vast majority of our cases."
"What we have now set out is a plan for us to see a decline and get Covid-19 back under control and we have done it before we've reached an escalation point - a point of almost no return when transmission takes off so significantly that you see your health system not cope."
Ardern said she hoped to ease some restrictions in some places after the end of the lockdown period in four weeks' time, even if there were some areas of concern.
At that point, it would mean a continued emphasis on the 'stamp out' stage where cases will be managed for as long as a vaccine is sought, she said.
Her message to New Zealanders as the country prepares to move to level four: "Stay home."
She asked people to build connections with those around them and stay in contact with loved ones, including elderly individuals who may need to have a support plan in place.
The Prime Minister told Morning Report the Government was moving to ensure people didn't have escalating costs on their income in a period of uncertainty.
On Monday, Finance Minister Grant Robertson announced that Cabinet would remove the $150,000 wage cap for all businesses, and there would be no rent increases and support for mortgage holders.
"There are stark choices here, we sat down as a Cabinet yesterday and considered the fact that if we didn't take the measures we're taking today, and that all New Zealanders are taking, then we could lose tens of thousands of people's lives," Ardern said.
"Our view is we also can do much more to try and stop people losing their livelihoods - we extended the wage subsidy, there's now no cap, so every business is able to access that support for every employee, we hope that will support people through the next period of disruption."
Ardern said the minister had met with banks to seek assurances that people would not be losing their homes as a result of employment and income issues from Covid-19.
She said the minister is also working through a similar scheme with banks like in Australia for business guarantee, and an announcement on that could be expected soon.