Director-General of Health Ashley Bloomfield said there were no new cases to report from managed isolation.
The one new case that remains under investigation is in addition to the one case yesterday that is being investigated.
"But in both cases we feel quite confident that they will be linked to the outbreak."
He said 54 people linked to the cluster have been moved to a quarantine facility, including 24 of the people who have tested positive.
The seven new cases reported today bring the total number of confirmed cases to 1258.
Hipkins said the fact the new cases were connected to one cluster was heartening and "we can be confident we can put a ring around the cases".
He said there had been no positive cases from the border testing.
The new cases were following a reasonably predictable pattern, said Hipkins, and it all pointed to a contained outbreak.
The number of active cases in NZ is 56, of which 37 are from the community outbreak and 19 are imported cases in quarantine.
The national contact tracing service has 1090 close contacts identified and 934 of those had been contacted by 10am this morning, Dr Bloomfield said.
Test results from the Kingswood rest home facility in Morrinsville that have been done so far have come back negative from all staff and residents.
Dr Bloomfield said the two people who have tested positive for COVID-19 in Tokoroa are being transferred to the Auckland quarantine facility and their whānau and close contacts are in self-isolation and they are receiving support.
Hipkins said testing was on track to test every border worker by the end of Monday.
So far 583 managed isolation and quarantine staff, 986 airport and 270 maritime staff have been tested.
Hipkins said he accepts responsibility for the lack of testing at the border, but stopped short of apologising.
There are two investigations underway on international travellers - one who turned up in Japan with COVID-19 on arrival and one who travelled to Belgium and tested positive on arrival.
Dr Bloomfield said the Japanese traveller left New Zealand on 8 August and transited through Singapore to Japan and the other is someone who travelled to Belgium on 6 August and transited though Singapore via Amsterdam.
Both cases are considered low-risk and Dr Bloomfield said contact tracing was being done.
On travel exemptions on the Auckland border, Dr Bloomfield said they had received more than 100 requests. All have been acknowledged and 45 have been approved.
Details about the exemptions are on the Ministry of Health website.
Dr Bloomfield said masks were now available out in the community.
Hipkins also said the government was working with Auckland schools to distribute devices and packs of education material to students who need it.
He said the packs of materials were waiting in a warehouse.
"I am concerned about those NCEA students I do want to acknowledge that they have had a very difficult year. We will be looking very closely at that in coming days."
Yesterday Prime Minister Jacinda Ardern announced that Auckland will remain in alert level 3 while the rest of the country remains at level 2.
The current alert levels will remain until 11.59pm on 26 August, but will be reviewed on 21 August.
There were 12 new COVID-19 cases announced yesterday and one probable case.
Today epidemiologist Sir David Skegg told RNZ's Kim Hill that New Zealand needs to dramatically improve its pandemic response if it is to avoid going in to lockdown every time there is an outbreak.
And Hipkins told Kim Hill that in reviewing the lockdown next week, they will be looking at the spread of the virus outside of Auckland, cases without a clear link to the existing cluster, and finding a likely source of the cluster. They would also be looking at genome sequencing and results of testing on border staff, he said.