Four people aboard a cruise ship that berthed in Australia and had also visited New Zealand have tested positive for coronavirus.

Other passengers who may have been exposed have disembarked the ship, which berthed in Sydney on Thursday morning.

One confirmed case is a staff member who was allowed to board another cruise with a new group of passengers that is at sea between Sydney and Wollongong.

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

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KATE GERAGHTY/SMH Ruby Princess cruise passengers arrived in Australia five days ahead of schedule after the government urged overseas Australians to return home.

The ship travelled to Fiordland (11 March), Dunedin (12 March), Akaroa (13 March), Wellington (14 March) and Napier (15 March). The cruise was shortened after visiting Napier, for weather reasons, and the ship returned directly to Sydney and passengers disembarked on the 18 March.

The Ruby Princess had been due to arrive at Tauranga early on Monday morning but it's redirection to Australia meant it bypassed its scheduled visits to both Tauranga and Auckland.

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.

New South Wales Health Minister Brad Hazzard is urging all 2700 passengers and 1100 crew who were on board the Ruby Princess that arrived at 6am from New Zealand to self-isolate immediately.

It is possible other passengers who disembarked in Sydney unknowingly contracted coronavirus, Hazzard said.

"Our big concern, the very big concern, is that those people came off the cruise with no knowledge of Covid[-19] actually being on their ship," he said.

"If they think that it's not necessary to do the 14 days, and if they think that it's okay to be wandering around, the clear message from me as New South Wales Health Minister is, no, it's not."

Two passengers aged in their 70s are being treated in the dedicated Covid-19 ward at Royal Prince Alfred Hospital. One patient is severely unwell.

A third passenger has also been diagnosed with the disease and travelled to Tasmania.

Chief Health Officer Kerry Chant said all passengers have been sent emails and text messages alerting them to the situation and directing them to self-isolate.

Several passengers developed flu-like symptoms while at sea. A doctor on-board swabbed 13 passengers and checked for Covid-19 once the ship arrived in Sydney. All passengers were allowed to disembark.

The Princess cruise line also operates the Diamond Princess vessel on which almost 700 people contracted coronavirus when it was quarantined in Japan for two weeks in February.

And a passenger who was on the Golden Princess, which docked in Akaroa last week, was tested but the result was negative.

The number of confirmed coronavirus cases in NSW jumped by 75 to 382 in the 24 hours since 11am on Thursday - the biggest jump to date

Four other confirmed cases of Covid-19 are close contacts of people who attended a Sydney Church of Christ service at Ryde Civic Centre on March 8, Chant said.

Chant urged the 300 attendees at the service to monitor for symptoms for the next two days, as their chance of having Covid-19 is "slightly increased".

"I can confirm that we have contacted all of the close contacts of the confirmed cases that attended that service," Chant said.

"But given the fact that, in such a big service of around 300 people, it's hard to absolutely exclude who's contacted who. We are wanting to put the whole group of people that attended that service on notice."

- with Sydney Morning Herald