New Zealand has its eighth case of the coronavirus, after two new cases were confirmed to have been brought in by travelers just as the country ushers in tough border restrictions. 

The two new cases were confirmed by officials about 2.30pm local time Sunday (the country's sixth case had been confirmed only the day prior); both involved recent arrivals. 

"New Zealand now has eight cases of [coronavirus] based on laboratory testing," the country’s Director General of Health, Dr. Ashley Bloomfield, confirmed in a press conference that was streamed live.

The news comes a day after Prime Minister Jacinda Ardern announced what were said to be among the world’s toughest measures for quarantining incoming visitors to the country.

One case involved a woman in her 30s from Denmark who had traveled to New Zealand from the U.A.E. five days ago. 

The infected patient had arrived in Auckland via Doha on March 10 before travelling to the city of Christchurch and then to Queenstown. The woman is being treated in a local hospital but her prognosis is positive, Dr. Bloomfield said. 

A second case involved an Australian man in his 60s who arrived in Wellington in the early hours of Saturday morning after flying in from Brisbane but who had already been tested in Australia before departing.

"Once informed of [...] his positive test our public health authorities kicked into action to find that person," Dr. Bloomfield said. 

It is unclear what advice physicians had given the man before departing Australia and the matter would be investigated, Dr. Bloomfield said. 

The man was in self-isolation with a partner, was symptom free and did not need hospital treatment, Dr. Bloomfield said. 

The man was said to have patronised a local cafe but Dr. Bloomfield said he was not aware that he had come into close contact with anyone while doing so. 

Close contacts of both cases are being tracked down by public authorities.

Authorities are now advising people on the same flights to make contact with local authorities to establish if they came into close contact with either patient, Dr. Bloomfield said. 

From Monday all passengers incoming to New Zealand, except for those travelling from the Pacific Islands, will have to self-quarantine for a period of two weeks upon arrival in the country. 

"We are currently finalising some further advice on [limiting mass gatherings]," Dr. Bloomfield said. 

The new requirements will be presented to Cabinet for considering on Monday.

"The requirement is that anyone coming into the country [...] will need to go into self-isolation.

"We've got this window of opportunity to support our health system so that we can get through this."

Ms. Ardern is expected to announce an economic stimulus package to help the country counter the forecast economic downturn from the virus later this week; the largest, she said, in her premiership.