Ayesha Verrall says further testing of people who were at locations of interest will help to paint a picture of if and where there is Covid-19 community transmission.
The Associate Health Minister told Breakfast on Monday contact tracers were doing an excellent job in tracking down 10,000 contacts or people at locations of interest.
Follow up test results for some of the thousands of people are due in coming days.
"Many of them are coming up to the point we're they're about to have tests due so in the next few days we'll start to get a better picture of the locations of interest at which transmission has occurred," she said.
"So far it's been a minority of them."
Verrall's comments come as Cabinet today meets to discuss New Zealand's alert levels.
The country will be updated at 4pm today on whether New Zealand will stay at Covid-19 Alert Level 4 post-Tuesday night, or if there will be any changes.
Prime Minister Jacinda Ardern announced on Friday that the entire country would remain at Alert Level 4 until at least Tuesday at 11.59pm - in line with Auckland and the Coromandel. She said this would be reviewed on Monday.
New Zealand went into Alert Level 4 at 11.59pm on August 17, initially for at least a week for Auckland and the Coromandel and three-days for the rest of the country.
However, Verrall wouldn't hint at if lockdown would be extended when questioned Monday morning.
"When I look at the situation we have some reassuring news, but also some risks," she said.
"So the reassuring thing is that when we identify new cases they're all linked very promptly to the outbreak. The second thing is that we've had excellent levels of testing and our testing staff have performed phenomenally, both in the community and at labs."
Five per cent of the Auckland population has been tested this outbreak, that's compared to a goal of one million for previous outbreaks, Verrall said.
"It's just been a massive scale up.
"It makes me feel very optimistic that the outbreak is not at the upper end of the estimates we had when we first started, but we're not out of the woods, we're still finding new cases and then we've got to make sure that their contacts are isolated so we still have a lot of work to do, particularly in Auckland."
Verrall said the current risks were that new cases continue to emerge in the community, as well as that not everyone who has been at a location of interest is known.
She noted that tens of thousands of people had left Auckland between the time community transmission began and the country went into lockdown.
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