They are the mystery cases pivotal to figuring out when Auckland might exit lockdown.

A public health expert earlier today warned "unlinked" cases could keep the city at New Zealand's highest Covid-19 alert level beyond next Tuesday.

And this afternoon's Government press conference showed more new mystery cases had emerged.

Director general of health Dr Ashley Bloomfield said today there were six new unlinked cases, bringing the total of mystery cases in the outbreak to 29.

These cases - where a link has not been established to previous positive cases - are a tiny minority in the total outbreak of 879 cases.

"They're definitely numbers to watch, but difficult numbers to interpret," Covid-19 modeller and physicist Professor Shaun Hendy said this afternoon.

"Often with the new cases, it just takes time to establish what these links are."

Sometimes, the cases were just too new, or the information hadn't flowed through to the health czar in Wellington before the 1pm press conference.

But after a while, anxieties would grow if no links were established.

"If they haven't found the links over 24, 48 hours, then there starts to be a bit of concern," Hendy told the Herald.

"Unlinked cases that are quite old are less of a concern. After about a week, it's probably not a big deal."

When that much time had passed, authorities had often gathered information on other community cases or sub-clusters to provide a better picture of the outbreak.

Earlier today, epidemiologist Professor Michael Baker said Auckland needed a few days without unexpected cases before confidently shifting to alert level 3.

"The two things we are particularly looking at are obviously a decline in cases - we have to get into single digits - the other thing that's important are unexpected cases."

Expected cases were close contacts and household members of previously identified cases. Unexpected cases were those with no obvious exposure.

Baker said unexpected cases suggested undetected lines of transmission might exist in the community.

Bloomfield this afternoon said the unlinked cases included two from Middlemore Hospital in Ōtāhuhu, South Auckland.

Bloomfield said two cases in one household had different mutations, which suggested an intermediate case in between the two.

Officials were now trying to find the person who might be that intermediate case.

Deputy Prime Minister Grant Robertson said Cabinet was looking for links but if testing was high and case numbers were falling, that likely indicated undetected chains of transmission weren't raging.

But Robertson said a high number of mystery cases would make an alert level reduction more difficult.

The Deputy PM said the strategy was about "being careful, but also being sure that when we do a job we do it once, and we do it right".

Not everyone worldwide is treating unlinked cases as such a priority.

In Singapore, health authorities this week announced an end to publicising mystery case numbers.

But that was because Singapore had now moved to treating Covid-19 as endemic, The Straits Times reported.

It was also increasingly difficult to trace links between cases now that vaccination rates in Singapore were high, a public health expert told The Straits Times.