Minister of Health Chris Hipkins says alert level 3 restrictions in Auckland are helping get to the bottom of the cluster and the city would not go into level 4.
Following the positive case of the hotel maintenance worker, health officials are being urged to use serology testing which could reveal if a person has had the disease even if they haven't had a positive Covid test.
Hipkins said serology tests were used but not routinely.
He told Morning Report it had been used for the Auckland cluster but wasn't sure if the test had been used for the Rydges Hotel maintenance worker.
"We use it where it can help us to slot new pieces into the puzzle."
He said the Government didn't yet have a good understanding of how the hotel maintenance worker caught Covid-19.
"It remains a bit of a mystery."
At this stage, he couldn't rule anything out - "surface transfer certainly possible", he said adding that an investigation was still ongoing.
So far tests of all co-workers, close contacts, family and household have returned negative results, Hipkins said.
"That's promising ... we got that one early enough that it hasn't been passed on or if it has been passed on, it won't spread further because we've isolated all the people that person could have potentially passed it on to."
He said the workmates would be tested again, but a decision on testing the household members again was yet to be made.
"We'll be making sure there's no risk of any of those contacts passing it on to someone else if they've picked that up."
He said everyone at the facility was being tested, and if there was a spread, it would have almost certainly showed up in testing results.
"This is the system as it should operate."
Hipkins ruled out Auckland moving to alert level 4.
That's because there was no spread at the Rydges Hotel, and though there was an unidentified spread of the "Auckland August cluster", the Government was trying to get ahead of it.
He said level 3 restrictions were helping get to the bottom of the cluster.
However, National Party leader Judith Collins would not say if Auckland should stay in level 3 or not.
Covid-19 border controls were front and centre yesterday in the first sitting of Parliament since the postponement of the election.
Collins told Morning Report not testing all border staff was "a massive failure" for the government.
"I'm not going to blame [director-general of health] Dr [Ashley] Bloomfield."
Collins said Prime Minister Jacinda Ardern should take responsibility, first for letting David Clark stay on as health minister for three months, and then appointing Chris Hipkins - who already holds several portfolios - as the new minister.
"The buck stops at the top and it stops with her. She's responsible, she needs to explain it.
"You don't, as prime minister, put out a press release on June 23 saying we're testing frontline staff at the border and then find out eight weeks later ... the public finds out that was not true."
Collins said there should be mandatory testing for border staff.
"Once every two weeks is better."
She said National health spokesperson Shane Reti had advised her that about 30 per cent of tests could return false negative results, which is why she said frequent testing was necessary.
"It's not just about testing, it's also about contact tracing."
She said the government's NZ Covid Tracer was not working competently and only 6 per cent of the population was currently using it.
"We will be putting out our policy in relation to this," she said.
By 1pm yesterday afternoon, Bloomfield said nearly 1.5 million people, or 37 per cent of the population, had downloaded the app.
Collins said people risked losing their jobs after a "total and systemic failure at the border".
"What I believe is that when Covid-19 comes in through the border that we have to have a system in place that immediately can find out where this has gone."