Director-General of Health Ashley Bloomfield has confirmed New Zealand's seventh and eighth positive Covid-19 coronavirus cases.

Both of those cases have overseas links, Bloomfield said.

The seventh case was a man in Wellington, who came from Australia and has tested positive. He arrived at 12.05am yesterday morning from Brisbane on Air NZ flight 828.

He was self-isolating with his partner and another family member, and was symptom-free. He does not need hospital treatment.

The eighth case was a woman travelling from Denmark via Doha on flight QR920, arriving on March 10.

She flew from Auckland to Christchurch on Jetstar JQ225, and she then travelled to Queenstown in a private rental car.

She was unwell upon arriving in Queenstown and was in hospital. She was recovering well and planning was underway for her discharge.

People on the same flights as the seventh and eighth cases should contact Healthline - 0800 358 5453 - to see if they were in close contact with the positive cases.

The fact that these two more confirmed cases had travelled from overseas reinforced the imporatnce of the new travel restrictions, announced yesterday, for all people coming to New Zealand to self-isolate for 14 days - which kicks in at 1am tonight, Bloomfield said.

Bloomfield said close contacts were being identified, and those identified were in self-isolation for 14 days.

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All previous confirmed cases have now recovered or are recovering at home, Bloomfield said.

Three people have also been isolated on a crusie ship in Akaroa, and were being tested.

Two of them were in close contact with a previously confirmed case, one of whom had symptoms.

All on board are not allowed off the ship until those test results are known, he said.

Bloomfield thanked the New Zealanders who had been through self-isolation in the last four to six weeks, and work is underway to "scale-up" the response as the number of those in self-isolation was expected to ramp up.

The only infections in New Zealand were within family members, he said.

Latest studies showed that people can be infectious in the early stages of getting Covid-19, he said, and the most common way of getting infected was being in repeated close contact with someone who had it.

That reinforced the importance of staying at home if you're feeling unwell, he said.

That would allow the health system to be able to cope with the number of cases as they came up, he said.

Bloomfield is giving the media conference in Christchurch alongside Canterbury DHB Chief Medical Officer Dr Sue Nightingale.

Nightingale said the DHB was looking at how to manage its staff, including vulnerable staff, as well as setting up community-based clinics, which should be ready by Wednesday.

She said testing capacity would also be ramped up, including two shifts of staff on from tomorrow so that testing could take place twice a day.

Contact tracing was essential to "flattening the curve" to keep people out of hospital as much as possible, she said, which would enable hospitals to better respond to acute health needs.

Bloomfield said Healthline had triple the number of calls as they did on the same day last year, and he asked callers to be patient. "Don't ring if it's just for general information."

He said self-isolation for positive cases and close contacts needed to be strict, but others returning to New Zealand from overseas didn't need to be.

Those people didn't have to stay in their rooms, but they shouldn't go to public places.

Close contact, he said, was now aligned to other countries to within two metres of a positive case for more than 15 minutes; previously it was within 1.5 metres.

He said there was lots of testing capacity in New Zealand, but people who were anxious but didn't have any symptoms would not be tested.

He added that social distancing didn't mean social isolation, which was more about physical distance. But people should be remain socially connected, and should check on each other, particularly the most vulnerable.

Asked about the cruise ship off Akaroa, Bloomfield said he would wait for the test results to come back. He noted that the new travel restrictions meant that no cruise ships can come to New Zealand until at least the end of June.

Some cruise ship passengers may have previously disembarked in Dunedin, but Bloomfield said the main concern was for people on the cruise ship.

But he would not be drawn on what might happen until the test results came back.

Yesterday a sixth case was confirmed, and this morning the seventh case told the Herald he was self-isolating in a hotel room in Wellington - the first case outside Auckland.

The sixth case, a man in his 60s, recently returned to New Zealand from New Jersey in the United States and is at home recovering in self-isolation.

Flying home from New Jersey via Houston, no one else on the flight should be alarmed because they were not regarded as being in close contact.

That's because the man did not start feeling unwell until more than three days after he arrived back in the country, the Ministry of Health said in a statement.

The man did attend a church service at St Mary's church on East St, Papakura, on Sunday March 8 at 8.30am before he became unwell. Attendees were on Saturday afternoon in the process of being contacted.

Family contacts of the man would also be offered testing and contact tracing was under way in Auckland, the ministry said.

The sixth confirmed case would be monitored daily by health services.

After starting to feel ill, the man did everything right by phoning ahead to his doctor and telling them of his travel history, about a possible link and his symptoms.

He was then assessed in his car by his GP, who was wearing the appropriate protective equipment.

Protective gear, which includes a gown, goggles, face mask, and gloves had been sent to 420 GP practices across Auckland.

The two previous patients in hospital - one confirmed case and another probable - were now back at home and recovering. Daily checks are being undertaken on the two by health staff.

All close contacts of the other five confirmed cases - 252 total - were in self-isolation and were also being monitored daily by health staff, the ministry said.

Community members who were sick have been asked to stay at home and not head out to public events or even work.

The advice for the public remained the same, the ministry said.

Anyone feeling unwell should ring Healthline on the dedicated Covid-19 number: 0800 358 5453 or alert their GP who would advise them.