Deputy Prime Minister Winston Peters says Cabinet is considering a law change to make masks mandatory in Auckland.
He told Mike Hosking Aucklanders should be wearing a mask whenever they leave home.
"The encouragement is to go out and get masks, and make sure when you are out you put them on."
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.