Six people in New Zealand have now tested positive for coronavirus.

The chief executive of Waitematā District Health Board Dr Dale Bramley confirmed the news on Saturday.

The person is an Auckland man in his 60s who recently travelled back to New Zealand from the United States.

Bramley said he received confirmation of the sixth case on Friday night.

He said the new case repeats the previous pattern of people returning from overseas, and officials were working very quickly to isolate the case and contact close contacts.

He said there was still no community spread.

"We understand the man was in New Jersey, travelled home via Houston to New Zealand," Bramley said.

A Ministry of Health statement said the man had been unwell and was now recovering at home. Hospital treatment was not required.

He will recover at home in self isolation and will be monitored daily by health services.

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The man returned recently from the United States, where there is local transmission of Covid-19.

It was more than three days after he arrived back home before he became unwell. The public health assessment was that no-one else on the flight was considered to be a close contact.

His partner who travelled with him was well, and was also in self isolation.

Once he became unwell, the man did everything right, the Ministry said.

When friends in the USA alerted him to their possible link to a Covid-19 case in the US, on Wednesday he phoned ahead to his doctor and told them of his travel history and his symptoms.

The man was then assessed in his car by his GP, with the GP wearing appropriate protective equipment, and a test swab was taken.

The man, who first started feeling unwell at the beginning of the week, has improved considerably and now reports feeling almost completely recovered, the statement said.

Family contacts of the man will be offered testing and contact tracing is now under way in Auckland.

The man was involved in a church service not long before he became unwell. As a precaution public health services regard those present mostly as casual contacts but a handful of close contacts at the service are being contacted and put into monitored self-isolation.

People attending the 8.30am service on Sunday, March 8 at St Mary's church in East St Papakura are now in the process of being contacted.

The majority will be advised that there is no need to be in self isolation but they should contact Healthline or ring ahead to their GP if they become unwell.

A statement from Catholic Bishop of Auckland, Bishop Patrick Dunn, said he was advised of the case on Saturday.

"The parishioner appeared well and showed no symptoms of any illness," Bishop Dunn said. "The person became ill during the week."

Dunn said the church was contacting parishioners, especially those who attended the same Mass as the person. Older parishioners and those whose health might not be the best were being particularly contacted.

"I am advised by health experts that the risk to others at that Mass of contracting Covid-19 is low," Dunn said. "This is because the risk of Covid-19 being passed on by someone not showing symptoms is regarded as low.

"The wellbeing of our parishioners is our first priority, which is why we started to contact them as soon as we became aware today that a parishioner had been diagnosed with Covid-19," he said.

Dunn said Saturday's 5pm Vigil Mass at St Mary's and the 8.30am and 10.30am Masses on Sunday would go ahead as planned, because the risk of transmission was regarded as low for persons without symptoms.

At Saturday's press conference Bramley advised members of the public who were feeling sick to not go to public events.

If you are unwell, do not go to work. It is important that message is very clear, he said.

He said New Zealand was not in the same position as Australia, with the amount of cases we have and the position we are in.

Bramley said 420 of GP practices in Auckland had been sent protective gear. They had to make sure they had all of the relevant equipment and to ensure safe testing to protect primary care workers.

In the future there could be more testing and more gear needed, but at the moment this is a dynamic situation and will be reassessed, he said.

New Zealand has so far had six confirmed cases and two probable cases of the Covid-19 coronavirus.

There are now 132,758 cases of the virus globally and 4955 deaths.