More than 50 New Zealanders are being contacted after four people on their cruise ship which made a stop in Wellington tested positive for coronavirus.

Nearly 4000 passengers and crew were on cruise ship Ruby Princess which left from Sydney and was docked in Wellington last Saturday.

New South Wales health minister Brad Hazzard told Australian media that people on board the ship had flu-like symptoms.

Although 13  people were swabbed, about 2700 passengers were able to walk around Wellington and visited popular tourist sites.

The Ruby Princess left Sydney on March 8 travelling to Wellington on March 13, Napier on March 14 and Sydney on March 18. 

It was supposed to arrive in Tauranga on Monday morning but was re-directed to Australia, bypassing its visits to Tauranga and Auckland.

In a release, the Ministry of Health said it was contacting 56 New Zealanders who were on board the ship.

"While in Wellington, there were a small number of passengers on board at the time with flu-like symptoms, and five passengers were tested in Wellington for COVID-19 on March 14.

"These people never left the ship in Wellington. The results from those tests were negative."

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The Ministry of Health was in the process of contacting the 56 New Zealanders who were on board the ship.

"Any passengers on the cruise, who have since returned to New Zealand, would be covered by the requirement since 15 March for all travellers returning to New Zealand to go into self-isolation for 14 days."

The ministry is working with Customs and the Ministry for Foreign Affairs and Trade to check whether New Zealanders on board have now returned to New Zealand."

All returned passengers would now be treated as close contacts and followed up with daily health checks, the ministry said.

The ship travelled to Fiordland, Dunedin, Akaroa, Wellington and Napier but the trip was shortened after visiting Napier, for weather reasons, and the ship returned directly to Sydney. Passengers disembarked on the 18th.

"The Ministry of Health is working through the itinerary of local visits undertaken by passengers to see if there are other precautionary steps that need to be taken.

"Ministry staff will also be working with their counterparts in Australia to determine – from the four cases with covid-19 – any other possible close contacts in New Zealand that will be contacted, put into self-isolation and tested if showing symptoms."

A CentrePort Wellington spokesman said the cruise ship had a full health clearance by Regional Public Health and redirected questions to the organisation. 

Regional Public Health has been contacted for comment. 

Health authorities were now trying to contact the passengers but it had been "a bit of a journey" as some had not responded, he said.

Passengers would be told to self-isolate for 14 days and to report if they had any flu-like symptoms. 

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"It is actually serious, because if we have nearly 2700 people that were passengers on that ship, we want to know every single one of them is in quarantine."

"I'm asking the media to get that message out to the community. And to the community: If you know somebody who came in yesterday from the Ruby Princess, do our community a very big favour and have a chat and make sure that they are given this clear message.

"Put yourself in a self-isolation. Follow the rules, and if you're feeling ill, any of the symptoms that might be related to covid-19, then make sure you contact a medical practitioner, either your local GP or the local ED in the hospital, and then take advice on what you should be doing."

The Ruby Princess had already left Sydney and was currently at sea, off the New South Wales coast.

As of Friday, New Zealand has 39 cases of coronavirus.

Ministry of Health director-general of health Ashley Bloomfield said of the 11, five were in Auckland, two in Waikato, two in Wellington and one in Canterbury and Hawke's Bay.

The new cases were associated with overseas travel, rather than community spread.