Five hundred more Defence Force staff are being deployed to managed isolation facilities to roll out the testing of staff quicker.
The Government is also directly hiring security guards to help control the facilities, which will make them less reliant on private security guards.
It comes as officials report six new cases of Covid-19 today, one of which is in managed isolation.
The other five cases are in the community, all linked to the South Auckland cluster, while 23,038 tests were processed yesterday.
There are no new cases linked to the Rydges Hotel case.
Prime Minister Jacinda Ardern said today's results were "encouraging" and there appeared to be no surge in cases in the community.
There was "no intention to move to level 4, and no need to" based on test results so far.
'No system is foolproof' - PM
She said Cabinet's testing strategy from late June - to regularly test all border-facing workers - had not been executed as expected.
She outlined three new measures to bolster its implementation.
A small team will be set up to support the Health Ministry, co-chaired by Heather Simpson and Sir Brian Roche, with the testing strategy.
"We are implementing here a strategy that cuts across multiple government agencies. Health is deeply embedded in the roll out and we do need to support them."
Secondly, Roche was also working alongside Auckland's public health unit, and he will report to director general of health Ashley Bloomfield on progress.
"This will raise accountability and will give more central control over procedures."
The third measure was the deployment of 500 more Defence Force staff to managed isolation facilities.
That will bring the total Defence Force personnel supporting the Covid-19 response to around 1200 – the largest military contingent since Timor-Leste.
This boost will be rolled out over the next six weeks, and staff at each facility will be 19 per facility.
The measures weren't a sign that the testing strategy wasn't properly resourced, she said, but rather that it was a complex operation.
Some 40,000 Kiwis had returned from overseas, and it was "unrealistic" to have a perfect border system, she said.
The measures would help limit the risk of further spread. "No system is foolproof and in a global pandemic, there are no absolutes."
Bloomfield welcomed the extra Defence Force staff and didn't see it as a vote of no confidence.
He said he would have liked the testing strategy of border-facing workers to have been rolled out at a faster rate, a sentiment Ardern and Health Minister Chris Hipkins have previously expressed.
He had not asked why his Ministry had told Hipkins that there was weekly testing at the Jet Park Hotel several weeks ago when that wasn't happening.
He had been focusing on the response to the outbreak but would look into why that had happened in due course.
Bloomfield said it might be worth looking at tightening level 1, including more mask use and physical distancing.
Ardern wouldn't be drawn on whether level 1 should be tightened and she had not talked to Bloomfield about that.
Breakdown of 1200 Defence Force personnel:
• 990 at Managed Isolation Facilities
• 80 at Border
• 70 in Police Traffic Management
• 100 for electoral support.
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There are 125 people linked to the Auckland cluster who have been moved into the Auckland quarantine facility, including positive cases and household contacts.
There have been 1299 confirmed cases in New Zealand.
There are five people receiving hospital-level care, one in Auckland City Hospital and four in Middlemore.
Since August 11, there have been 1983 close contacts identified, of which 1861 have been contacted.
Bloomfield said the Glen Innes Pak N Save was only visited once by a confirmed case on August 12, and he apologised for giving different information yesterday.
He had given false information about casual contacts attending a fitness class the previous day, and had previously incorrectly pinpointed Pakuranga College as a place where a positive case had been.
He said serology would be used at the Rydges Hotel to see if there was an intermediary who was infected by the person returning from the US who then might have passed Covid-19 on to a maintenance worker.
Another possibility is that she infected a surface that the worker then touched.
Ardern said there is no evidence that higher surveillance testing of Pasifika communities might have detected this outbreak earlier.
She said everyone had a role to play to counter rumours and misinformation, including online platforms such as Facebook.
The World Health Organisation could play a role in fighting misinformation, she said.
Businesses failing to display QR codes, which is now mandatory, could be fined about $300, Ardern said.
Ardern said there was no plan to mandate vaccination if and when a Covid-19 vaccine became available.