Health officials have not yet considered moving the country to alert level 1.
Cabinet Ministers will meet on Friday to review the alert level settings, which are set to expire on Sunday.
Auckland is at alert level 2.5, which means there are tighter restrictions on mass gatherings. The same rules do not apply for the rest of the country, which is at alert level 2.
At a Health Select Committee meeting this morning, New Zealand First MP Jenny Marcroft asked what criteria were being considered to move the country down to alert level 1.
Health Minister Chris Hipkins said there could still be cases in the community at the lowest two alert levels, as long as they were contained.
"The real test is different levels of containment at level two and at level one, rather than complete elimination before you'd move to alert level one.
"We [Cabinet] haven't yet considered any advice on a shift from level two to level one," Hipkins said.
Director General of Health Ashley Bloomfield said officials were not yet considering moving Auckland and the rest of the country to alert level 1.
Instead, the focus was on moving Auckland from alert level 2.5 to 2.
Level 2.5 in Auckland "won't last forever", Hipkins told the Committee, and was likely to change "soon".
Covid-19 messaging faux pas
Dr Bloomfield offered the Select Committee an explanation as to why hundred of thousands of Aucklanders were advised to get an unnecessary Covid-19 test.
Everyone in West and South Auckland was wrongly advised at the weekend to get a test, regardless of whether they were showing symptoms.
The unclear advice made Prime Minister Jacinda Ardern "incredibly angry" and work was being done to correct it, she said on Sunday.
Bloomfield said when social media messaging was prepared, key words were missed out, which lead to a "completely different" message being made public.
Border testing
A schedule for regular testing of border and managed isolation workers will be released by the end of the week, Hipkins told the Health Select Committee.
Workers at the highest risk will be tested weekly, he said. Lower risk workers will be tested fortnightly and those on the periphery could have monthly tests.
Shipping ports were the most complex places to conduct testing, "because of the nature of what they do and the huge volume of people that interact with the port," Hipkins said.
Many workers had next to no potential exposure, he said, while others had quite a high level.
Officials have been working with port companies to establish a testing regime.
"There are thousands of people there, many different employers trying to do the right thing, and [some have] quite irregular contact with the ports. So if you're a driver coming to and from the port, for example, you're not always going to be there at the same time.
"So we've been working to identify what are the peaks for when testing capability needs to be there. Shift changes are a good example," Hipkins said.