Chris Hipkins says the Ministry of Health is working with lawyers on making masks mandatory in Auckland.
The Minister of Health says the Government is moving swiftly after finding community transmission of Covid-19 in a bid to avoid a situation similar to that occurring in Victoria, Australia.
Hipkins told Morning Report it was impossible to move too hard, too soon.
He said the response has been precautionary and swift.
"One of the lessons from overseas is you can't be too hard, too soon, the faster you move the better your chances."
Hipkins said at this stage the restrictions were for three days, which will enable more information to be gathered, and at the end of this they will be able to determine a sensible course of action.
People in Auckland were being asked to wear masks if they were out in public either for essential travel or supermarket shopping, Hipkins said.
He said an order would be issued at midday today making mask wearing mandatory for Aucklanders was one of the things being considered.
Hipkins said the Government had been pushing to increase testing for Covid-19 up and in recent days had been getting around the desired 4000 mark.
He said at this stage the source of this outbreak was a puzzle.
"This person has no known contacts with anybody who has worked in managed isolation or at the border, they have no recent travel history themselves or contact with people who have travel history."
Hipkins said they would keep contact tracing until the source of the outbreak was discovered.
"Immediate family members have been tested, therefore we've got three additional positive results out of that, so therefore the contact tracing for those family members kicked into gear immediately, as soon as their positive results tests came in and we will just keep going until we identify where the source of the case is."
Testing will be undertaken at two workplaces, and Hipkins said he believed one of the children in the family attended Mt Albert Primary School.
But he said that child returned a negative test and at this point the health advice was that testing was not needed for everybody at that school.
Hipkins said at this stage they were in contact with anybody who had been in close contact with any of the four people who have tested positive for Covid-19.
"Getting them tested is our priority and then doing further contact tracing based on those results has been the priority."
Those who tested positive have been interviewed a number of times to determine who they have been in contact with and have been very cooperative, Hipkins said.
He said anybody who has symptoms and wants to get a Covid-19 test should phone the 0800 Healthline number first.
Hipkins said everybody who is leaving Auckland to return home today, they should stay home for the three days in the same way Aucklanders are being asked to.
He said police would help to enforce the level 3 restrictions in the greater Auckland area after midday today.
'We can do it again - but it's not easy' - Goff
The area for level 3 is the Auckland Super City boundaries - from Wellsford in the north to Pukekohe in the south.
Auckland Mayor Phil Goff said a police presence was likely on the borders of the area from today.
"The advice is clear, if you're outside of Auckland don't come into the city, if you are living in Auckland, you're not to go outside of the Auckland boundaries unless obviously you're an emergency or an essential worker."
He said Auckland did not want to replicate what happened in Melbourne.
"We really need to follow the rules, we need to nip this in the bud if we can as quickly as possible, we need at all costs to try to avoid the situation that they found in Melbourne where they took five weeks over it, they didn't lock down properly and we've seen the results of that."
Goff said it was going to be tough, but if the community outbreak were to get out of control it would mean a longer lockdown.
The level 3 restrictions were needed for as long as necessary, he said.
"I'm not pessimistic about it, we've been here before. By working together collectively, by being sensible, by following the rules, we defeated the spread of it better than any other country in the world did and we can do it again - but it's not easy."
Auckland Council is closing all of its community facilities such as libraries and swimming pools, effective immediately.
"Widespread testing and effective contact tracing will be the key to us defeating any further spread of this community outbreak."
• Aucklanders are being told to stay at home as the city goes into level 3 lockdown from midday today until midnight Friday
• The rest of New Zealand will move up to alert level 2 over the same time
• Four people in one South Auckland household test positive for Covid-19 from an unknown source
• A virus expert worries it may be tough to trace the source of the infection back to the border
• Supermarkets are calling for calm and urging people to 'shop normally'
• Auckland schools will only take students of essential workers – all others must stay home
• After praising our efforts to stamp out Covid-19, the world reacted to the sudden return of community transmission