One of the new cases is confirmed and the other probable.
The confirmed case is a student at Marist College, one of the country's biggest coronavirus clusters.
The student's only symptom was a loss of smell which wasn't significant enough for them to believe it was related to Covid-19 and their infection was only picked up as a result of the voluntary testing of 250 within the Marist College community.
Bloomfield said the test result was a "weak positive" so it was almost certainly very late in their illness.
But the significance of the weak positive test so late in the course of the illness is not fully understood.
While it was unlikely the student was still infectious, they would remain in isolation and be tested again next week.
The probable case was a household contact linked to the St Margaret's rest home cluster, Bloomfield said.
The two new cases bring the total in New Zealand since the pandemic began to 1488.
The low number of cases was encouraging, but Bloomfield repeated the message that we're not out of the woods.
"Failure to do so risks everything we have achieved so far, and we have all seen how quickly the virus can spread both here and overseas. Don't give it an inch."
Some of those stories didn't fit with her expectations of the health system during the lockdown.
"No one should go through that experience alone. Everyone should have been able to have a support person with them through that experience," Ardern said.
Bloomfield said the decisions came down to clinicians and DHBs and the Ministry of Health would work to understand what happened in each situation and that there was "every reasonable expecation of consistency".
"What we always aspire to is consistent where appropriate and different where appropriate."
He didn't agree that the Government failed those people.
Bloomfield said they would organise a flight if they needed to collect more medical supplies if needed after being asked about Pharmac reporting shortage of a specific drug.
On the lack of Maori representation in the Epidemic Response Committee, Ardern said there should have been a range of views represented but it was organised by the Opposition.
But the legal underpinnings for the lockdown and its enforcement were all in the public domain, Ardern said.
What Simon Bridges, who chairs the Epidemic Response Committee, was seeking was legal advice which he had strongly defended in the past when he was in Government, Ardern said.
Ardern said she'd been consistently advised there was no gap in the enforcement powers.
But the epidemic notices could have been more fit for purpose and there would be a time and a place in the future to re-look at that.
Ardern didn't rule out inviting Scott Morrison to join the New Zealand Cabinet meeting after joining the Australian Cabinet meeting yesterday.
Ardern said Australia and New Zealand were both on the same page and keen to open transtasman bubble but also to not be responsible for cases popping up in each other's countries.
The move to alert level 2
A smartphone app wasn't needed to move into alert level 2, as there could be other measures hospitality and retail sectors could use to ensure contact tracing, Ardern said.
Bloomfield said all of the apps had drawbacks and none were perfect, which was why it was so important for our gold-standard tracing.
One of the solutions could be a Bluetooth device, like the CovidCard, that people carry with them but that was still some time off.
Microsoft investment in NZ
Ardern said Microsoft's announcement to build a data centre in New Zealand served as a signal to the world New Zealand was open for business.
Building on investment opportunities would be part of our recovery, Ardern said.
"It is my view that by tackling the virus, we have positioned our economy to be able to rebuild ahead of many others globally. That is our safe haven strategic advantage."
International companies like Microsoft wouldn't be looking to invest here if they weren't confident in our response to Covid-19, she said
It was also a vote of confidence in our digital future, she said.
Ardern said the Microsoft investment was the result of a long-relationship, built through efforts like the Christchurch Call.
She said it wasn't at the expense of smaller, local companies.
On attracting other large companies, Ardern said there was a team within MIBIE to go out and invite other companies to encourage high-quality investment in New Zealand. Now was the time to do this work with extra enthusiasm as our response to get the message out there about our response to the crisis.
The 21 APEC economies have agreed to work together to ensure continued trade, investment and supply chains.
There were 3232 tests completed yesterday, with a combined total to date of 155,928.
Achieving zero cases two days in a row was testament to New Zealanders' efforts that "we can all be undeniably proud of", Ardern said.
But she urged Kiwis to double-down on their efforts to maintain the good run of numbers.
The Government will tomorrow release the rules for alert level 2 then decide on Monday whether to move down levels.
Deputy Prime Minister Winston Peters said this morning the details of the rules were still being worked through.
"We're looking at the total framework. You'll all have different views about it and they've got to be thrashed out," Peters told Newstalk ZB's Mike Hosking.
Bridges yesterday questioned Ardern in Parliament about the Government being too conservative about moving out of lockdown, causing business owners and workers to suffer.
Ardern gave Bridges a sharp rebuke by saying she was the one who had to be held accountable for her actions.
"That member may have the luxury of sitting on that side of the House, not bearing the consequences of a wrong move, but we do not. We have to factor in the livelihoods of every New Zealander."