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The ship, which was sailing around scenic Fiordland National Park, alerted local health authorities to the outbreak.
It is now on its way to Australia.
Dr Alistair Humphrey, Canterbury Medical Officer of Health said the Dawn Princess had its own doctor on board and the ship's crew were confident they could control the situation.
"The number of cases is declining. They're still seeing a few coming in but not as many," Dr Humphrey said this afternoon. "They stand at a little over 200 people altogether."
Local health authorities earlier ran tests on samples the ship provided, confirming it was a norovirus outbreak.
Dr Humphrey said ships were legally obliged to report any infectious disease outbreak to the local medical officer of health.
He said the ship alerted Wellington authorities to the issue late last week. That information was passed onto other public health units where the boat would dock.
Dr Humphrey said when the ship later docked at Akaroa, the local doctor was alerted, but there was no evidence any passenger spread the virus from the ship to the mainland.
"...The ship are making sure that people who are unwell stay on board in their cabins until they're well-recovered."
Dr Humphrey said norovirus outbreaks were common in rest homes, and spread rapidly in crowded places.
It could take days before an infected person's symptoms were obvious. "Generally speaking [patients] are most infectious when they're symptomatic, which is why it's important to keep people isolated in their cabins..."
The ship's owner Princess Cruises, a subsidiary of Carnival Corporation, confirmed some passengers on the current cruise reported gastrointestinal symptoms confirmed as norovirus.
"Most passengers on Dawn Princess are unaffected by the illness," the cruise line said in a statement today.
"It takes relatively few cases to be reported onboard for even more stringent sanitation levels to be implemented. This happened on Dawn Princess to contain any spread of the illness. The containment response worked effectively and the number of new cases declined significantly," the company added.
Some social media users discussing the outbreak blamed people who did not wash their hands properly after going to the toilet for spreading the virus.
Princess Cruises said its sanitation measures included closing all self-service in food areas and encouraging passengers to use their own cabin bathroom facilities.
The Cruise Law News blog said a similar "pukefest" happened on the 261m long ship two years ago. Then, 114 passengers and 11 crew fell ill.
A woman who claimed to have been a passenger on the ship during a previous outbreak said the crew responded efficiently last time.
"At such close quarters with such a large volume of humans anything is possible, it's just one of those things," she said on Facebook. "I found the operations of working crew to be very efficient and alert especially to problems that could arise from sloppy human behaviour."
Noroviruses caused stomach or intestinal infection, leading to vomiting and diarrhoea, according to the Ministry of Health.
The bug spread when people consumed contaminated food or drinks, or touched infected surfaces or objects and then stuck their fingers in their mouths.
"Norovirus is highly infectious and spreads easily from person to person. Both faeces and vomit are infectious, and the virus can survive on contaminated surfaces even after cleaning with some disinfectants," the ministry said on its website.
The ministry said people who shared food or ate from the same plate or cutlery as an infected person were also at risk.
Dawn Princess was on a 13-day cruise to New Zealand destinations and would leave the country today to return to Melbourne. The ship had 999 cabins.