The Ministry of Health is now assessing what it will do now with the 367 people it says it has tried "really hard" to contact after they left their managed isolation or quarantine.
Speaking to Mike Hosking on Newstalk ZB this morning, director general of health Dr Ashley Bloomfield says his team has sent "repeated texts, phone calls and emails" to those people but they were not getting back to them.
There were 2159 people who left managed isolation facilities between June 9 and 16.
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Of the 2159 people who left managed isolation facilities, 1284 people have now been contacted and have tested negative for Covid-19.
Eight hundred of these people were tested before leaving managed isolation and the remaining 484 were tested after departure from the facility.
There are 367 people who the ministry has repeatedly tried to make contact with but have had no luck tracking down.
"[They] are essentially not returning our calls. It is two weeks since they came out of their 14-day managed isolation so we're just having a think about what we do next."
Dr Bloomfield agreed with Hosking that contact tracing only worked if people were prepared to be contacted.
"We can do the best we can do but there are obligations on everybody to do their bit as well.
"We only started rolling the testing out from June 9. I'm really pleased we have and now we know from the 16th, people have only left the facility if they have been tested."
While that had been happening there had been no community transmission and the only positive cases were from people in managed facilities.
Asked whether the missing 367 offered zero chance of spreading Covid-19, Dr Bloomfield said he could "safely say that they do present a very low risk to the community".
"They all had completed the 14-day managed isolation so these people are a very low risk.
"They know what to do if they become symptomatic but we're not finding any Covid-19 out there, which is encouraging."
Asked about the 367 and why the ministry was unable to reach them and whether they had been giving false numbers, Dr Bloomfield said many had moved back to New Zealand without living here for a while so didn't have proper contact details.
"A lot of these people coming back to New Zealand have not lived here for a while, so their only phone number might be an international cellphone.
"Of course, they get out of quarantine, get a new sim card, we then don't have their phone number. They may not have a permanent address and may be staying friends or with family for a while. It's not straight forward."
He said people leaving quarantine were now being assigned their national health index number, with "a lot of effort" going into collating their contact information.
There was still a "real challenge" in regards to capacity and housing returnees but there was more coming, he said.
"Every single one of them needs to be looked after, we've got to do all the distancing and the testing right, so it's quite a big effort. There is more capacity coming online but, as reported at the weekend, there is strain there and that's what we're working to address."
As for reports of some doctors charging for Covid-19 tests, Dr Bloomfield said that should not be happening.
"No, the Government has put a good amount of funding to ensure that people who do need a test, can be tested, and that is free.
"People shouldn't be charged."