A fifth positive case of the new coronavirus has been confirmed in New Zealand - while a sixth case is "probable" after a woman's cruise-ship holiday in the US. Health officials have also confirmed a second probable case.

Director-General of Health Dr Ashley Bloomfield said on Saturday afternoon that the fifth confirmed case was a woman in her 40s - the partner of the third Covid-19 case confirmed in New Zealand.

She was already in self-isolation and did not require hospital-level care.

The US Government confirmed on Saturday that 21 people on the Grand Princess cruise ship, off the Californian coast, had also tested positive for coronavirus.

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Nineteen of them were crew members. The Ministry of Foreign Affairs and Trade says it is following up reports three crew members on the ship are New Zealanders.

An Mfat spokeswoman told the Herald it had not been contacted by any New Zealanders who may be on board.

Eight New Zealand passengers who were previously on board the cruise ship may have been in contact with a confirmed coronavirus case, the Ministry of Health has said.

All of them are now back in New Zealand. Bloomfield said five of them are well.

One of the other three, a woman in her 70s, was in North Shore Hospital.

After finishing the cruise, she had flown back from San Francisco to Auckland on Flight NZ7 (on February 25). She was admitted to hospital with a respiratory illness and tested for the virus but returned a negative result.

However, health officials now believe she is a probable case.

As a result, 43 hospital staff who came into close contact with her have been stood down for the remainder of the 14-day isolation period since they treated her.

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The ministry was also contacting people on the flight who were considered close contacts, and would ask them to self-isolate for the rest of the 14-day period.

Two other passengers from the cruise ship have mild symptoms. They had been tested, and one had returned a negative result.

In all, there have been 218 tests in New Zealand and five had returned positive. There were another two probable cases - the woman in her 70s and the grandfather of two people already confirmed to have the virus.

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The Ministry of Health confirmed on Friday that one of the people who had contracted the virus had attended a concert by American rock band Tool at Spark Arena in Auckland on the previous Friday.

The man had been in self-isolation since Wednesday and did not require hospital-level care.

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The ministry said the risks were very low for other people at the concert, and that attendees who were near the man should be aware of the symptoms and call Healthline if concerned.

The man was in the general admission section at Tool concert in the front left-hand corner of Spark Arena.

The Ministry of Health continues to support students and schools who have links to coronavirus patients.

On Thursday, the ministry confirmed the first person-to-person transmission of the virus inside New Zealand.

A family member of an infected man – and an Aucklander in his 40s – had been in Iran and returned to New Zealand on a Qatar Airlines flight from Doha to Auckland on February 23, flight number QR0920.