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The focus on supermarkets comes as New Zealand enters its fifth day of lockdown and has the first victim of Covid 19 - a West Coast woman who died in Grey Base Hospital yesterday.
The Cabinet meets again today and wants to ensure that supermarket supply chains, pricing, and customer and staff welfare are all up to scratch, given their importance to New Zealanders during the lockdown.
"We don't obviously have legal footing to enforce specials, but we can on price gouging," Ardern told Newstalk ZB's Mike Hosking this morning.
She added that the Government had seen no evidence of that so far.
She had been speaking to Consumer Affairs Minister Kris Faafoi, who had checked directly on claims of price-gouging of items such as cauliflowers.
While there had been issues of chickens being mistakenly weighted - and therefore mistakenly priced - and some supply issues, the Government had not found any price-gouging issues.
Ardern indicated she was keen on supermarkets opening on days that they were traditionally not allowed to, such as Good Friday and Easter Sunday, so as to give New Zealanders maximum access to food and essential supplies.
But she also wanted to check with supermarkets on whether they needed those days to help re-stock shelves. She said she would have more to say on supermarkets later today.
Ardern told Hosking the Government had resolved the issue of mixed messages over where people could and couldn't go in lockdown.
"I think the message around staying local has been clear... but no one has locked down New Zealand before. This is something we did in a 48-hour period. It wasn't always going to be perfect."
The Government was looking at the supply of products such as halal meat - and this was being resolved.
The Government and the Ministry of Business, Innovation and Employment (MBIE) had taken the approach of being as tight as possible on what represented essential services, and worked back from there.
Ardern and Director General of Health Ashley Bloomfield spoke about the chances of New Zealand coming down to level 3 in four weeks.
Bloomfield told Hosking that that might be possible if modelling showed the level 4 precautions were having a positive impact on the trend line of cases, and if, for example, New Zealand was returning to isolated cases.
Officials believe it will take around 10 days before we see any impact or trend from the lockdown rules, and whether they are working.
Ardern said it wasn't just the sheer number - but the type of cases. For example, if we got to the point of having 100% of cases originating from overseas cases, that was "under control somewhat" compared with other scenarios.
"We are still doing contact tracing on every case, even now."
Hospitals are now just half full, having cleared the decks of elective surgery and outpatient work to cope with a possible onslaught from Covid 19.