Ardern said the 61 new cases today seemed "heartening" on the face of it, but she said it was too early to say if the lockdown was slowing transmission. Transmission in the community prior to the lockdown may yet be "rearing its head".
The outgoing Police Commissioner has admitted police have failed to carry out the level of checks on recent arrivals to New Zealand, supposed to be in strict self-isolation, that had been promised by the Government.
Those coming here from other countries are one of the highest risk groups as potentialcarriers of the virus.
When people arrive at the border, they are quarantined if they have symptoms or don't have a plan for self-isolation.
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Those with no symptoms and who have a plan are sent home and told to self-isolate, which means no leaving the home or no close contact with anyone.
They are also required to alert authorities if they do develop symptoms, and to turn on the location setting on their phones.
Appearing in front of Parliament's epidemic committee via video link on his last day as commissioner, Mike Bush was questioned about the powers being used by the police under the level 4 alert, and how rigorous the checks are on people sent home to effectively self-quarantine.
Director-General of Health Ashley Bloomfield had said anyone sent home to self-isolate after arriving in New Zealand would receive a visit from the police within three days.
Bush admitted today that had not happened, and it was only in the last 24 hours that they had been able to contact "almost all" of those, by using technology.
He told MPs there are 1573 in hotels under "managed" self-isolation, with police and other security constantly present, and 116 in quarantine and being tested, with Covid-19 symptoms.
However, there are about 4000 people who were sent home to self-isolate after arriving here from overseas.
In the initial days it was "very difficult" for the police to find out where they were and make sure they were following the rules, Bush told the committee.
"In the last 48 hours, police and other government agencies have worked really well together to build a technology solution...in the last 24 hours almost all of those people have been checked on with the use of that technology."
There were also random checks, done in person by police officers.
If you have symptoms of the coronavirus, call the NZ Covid-19 Healthline on 0800 358 5453 (+64 9 358 5453 for international SIMs) or call your GP - don't show up at a medical centre It was the "intent" of the police to visit each person within the three days, said Bush, but they were unable to do that.
Given the extremely high risk of the thousands left to self-isolate at home, the committee chair and National Party leader Simon Bridges questioned whether the police had their priorities right.
"Wouldn't it be much better...if we policed quarantining rather more than we did, what neighbourhood people were in or what beach they're on?"
He was not dismissing the importance of that other work, but Bridges said limited resources should be prioritised.
Bush said he agreed it was an "absolute priority", but police needed to draw on technology first to get the necessary information out to frontline officers.
Until the tech system was created, the police were recording the number of visits to people's homes, said Bush, but there was not enough data to show whether they were "general compliance" checks, or for non-managed self-isolation.
There has been "no shortage of effort by everyone involved to get this right", he told MPs.
Bush also defended the "graduated" approach to lockdown enforcement and reassured the committee the police were applying their discretion fairly and consistently.
Earlier, public law expert Dr John Hopkins told the committee relying on police discretion without clear, transparent guidelines, is problematic.
"Relying on the discretion of individual officers, primarily police officers, is not in my view sustainable in the longer term. It risks conflict with such officers and Civil Defence personnel...this is particularly true as mixed messaging has been an issue in the first few days of the lockdown.
"We're now settling in for the long haul. To keep everybody on board requires a move away from the emergency phase and the natural instinct of leaders in an emergency to use discretion and instead create or publicise clear rules that are justifiable based on the evidence," Hopkins said.
Follow our live blog for all the latest coronavirus updates Bush said the focus on education, and then enforcement as a last resort was the right one.
He said that no one would be "prosecuted for being in doubt".
"We will only use those powers when people are persistent and seriously breaching that compliance. Our application of those powers will be tested in court," he said.
Bush acknowledged that historically police have not applied discretion fairly across communities.
