Jacinda Ardern says nearly 1000 people had sent in complaints about price-gouging at supermarkets after a dedicated email was set up.
Earlier this week, the Prime Minister told New Zealanders to report unfair high prices to the Ministry of Business, Innovation and Employment.
Ardern said at her daily press conference today - with Finance Minister Grant Robertson - that about 990 emails had so far been sent.
The most common complaint was about the high price of cauliflower - up to $13 each - but hand sanitiser, bread, meat, face masks and garlic also featured.
Those complaints would be taken seriously.
"The process for dealing with complaints is being worked through... and we will involve traders so they have a chance to respond."
Lifting the lockdown wouldn't happen until the virus was "back under control", and communities could stamp it out quickly when new cases arose.
She said the lockdown was asking a lot of New Zealanders, and they were mostly doing an "amazing job". Those who weren't taking it seriously needed to realise how important the lockdown rules were.
And she fired a warning to young people who thought they were less susceptible to Covid-19 and might have a more relaxed attitude to lockdown.
The 20- to 29-year-old age group was "far and away" the most affected by Covid-19, she said, and they could infect more vulnerable people.
"They are our vector for transmission."
Asked about Dr Lance O'Sullivan calling lockdown "a joke" in Kaitaia, Ardern said it was up to police to enforce the lockdown.
She checked in with police regularly to see if they had the resources to do their job, and the feedback was that they did.
Meanwhile, ministers Shane Jones, Phil Twyford and David Parker were all looking at how to get the jobless into jobs with "shovel-ready" projects, she said.
Work was also underway looking at how to speed up consents for development and infrastructure projects.
Robertson said a list of projects was being worked on.
The country's GDP could drop by as much as 17 per cent while unemployment could reach double digits, he said.
The prediction of 30 per cent unemployment by some economists was "extreme", and showed how uncertain the future of the economy was.
He said rent relief for commercial businesses was under discussion, and more will be said about that in a couple of days.
Media companies were struggling with the drop in advertising revenue, and Robertson said a unit in the Treasury was looking at what the Government could do, such as loans or equity purchases, to help essential services.
"The media is an area that sits in a broader set of recovery packages that we're looking at in the medium term."
Media companies were already under pressure before the lockdown and were hugely important, he said.
Ardern said the 61 new cases today - following a trend of fewer new cases each day - seemed "heartening" on the face of it, but it was too early to say if the lockdown was slowing transmission.
She said more testing would provide a fuller picture of community transmission, and the Government needed accurate information as soon as possible.
She said the Ministry of Health was looking at how to test in communities where little testing for Covid-19 had taken place.
Everyone who needed to be tested should be able to be tested, she said.
There were over 2000 tests today and the average over the last week was 1843 a day, though the number rose and dropped and needed to be consistently high, she said.
Testing capacity was always there, and there hadn't been a day where the number of test requests exceeded capacity.
GPs should also have enough swabs for testing, Ardern said. If they didn't, that would be a distribution, not a capacity issue.
Ardern said the $56m support package for Maori communities and the $27m for social service agencies - both previously announced - had allowed 11,000 care packages to be delivered so far, with 30,000 to be delivered by the end of the week.
The packages had also allowed Covid-19 testing for vulnerable communities.
Ardern said the package to help Maori communities was still being rolled out, and "where we see need, we will meet it".
About $12m of the $27m package had been given to agencies fighting domestic violence, she said.
Earlier today, Director of Public Health Caroline McElnay told media that there are now 708 confirmed and probable cases in New Zealand.
Fourteen people are in hospital, with two of those in ICU in a stable condition.
There are 82 people who have recovered. No further deaths have occurred.
McElnay said more than half of the cases were due to overseas travel, and about 1 per cent were community transmission.
But she conceded that the limits on the testing regime so far did little to show the true extent of Covid-19 community transmission in New Zealand.
A new directive to test more and looser testing criteria would lead to more tests, an increase in confirmed cases, and a clearer picture of the prevalence of Covid-19 in communities, she said.
The growth rate in the number of new cases continued to decline, with the announcement today of 61 new confirmed and probable Covid-19 cases in New Zealand.
But while that was "encouraging", McElnay said it was early days and more cases will spring up as testing capacity increased to 5000 tests a day.
Civil Defence director Sarah Stuart-Black said most people were still complying with the lockdown rules, but emergency powers had been used
Yesterday Ardern said she wanted more testing to be carried out, and Health Minister David Clark said this morning that 5000 tests per day would happen soon.
She also said that supermarkets will be able to open on Easter Sunday, but not Good Friday.
Yesterday about 1700 tests were done, even though there was capacity for about 3500 tests.
• Covid19.govt.nz: The Government's official Covid-19 advisory website
Expert epidemiologists including Sir David Klegg and Professor Michael Baker have been calling for more testing for weeks, saying that the previous testing criteria did not show the prevalence of Covid-19 in communities because it was too focused on close contact to confirmed cases or overseas travel.
The lockdown will only be lifted if community transmission has been stamped out, but making that call would be difficult without the testing to show where the virus is present.
