The two flights are from Guangzhou and Shanghai, both cities have confirmed cases of the virus. The virus is thought to have originated in animals and has killed 56 people since it broke out in Wuhan, Hubei.
Cases have been confirmed in Japan, Taiwan, Nepal, Thailand, Vietnam, Singapore, Australia, the US, and France.
People from the two flights to land were wearing face masks as they came into the international arrivals hall. One woman, Jennifer, told RNZ people were wearing the masks while on the plane.
Director of Public Health Dr Caroline McElnay said the news that had come in overnight that coronavirus could infect people during incubation had yet to be reviewed.
"That's not something we have been informed about officially. My team are looking at what we have received and exactly what the facts are in terms of what's known about infectivity before symptoms. Yes it makes it much more challenging to contain and manage this virus. But we need to be really clear about what the facts are.
"The nurses are there along with other public health staff to make sure people coming of the planes from China are aware of the symptoms of coronavirus. We expect that anyone off that plane is already well aware because they have come from China."
There is now a facility at the airport for people found to have high temperatures to be directed to.
One of the challenges for screening was that a high temperatures could be a symptom of other infections. At present it was influenza season in the Northern Hemisphere, and people with high temperatures were more likely to have the flu than coronavirus, McElnay said.
"It's a bit like looking for a needle in a haystack."
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The only test for coronavirus - a blood test - takes a couple of days for results to be returned, but New Zealand doesn't have the ability to do that test yet. Samples must be sent to Australia.
McElnay said the test would be available here later in the week.
She said the situation was being reviewed daily and the evolving situation was what led to the positioning of staff at the airport on Monday.
Information in Chinese languages and Chinese language speaking staff were on hand to help at the airport and via Healthline.
Up to 1800 people a day arrive in Auckland and Christchurch from China on six flights from Shanghai and Guangzhou. Both cities have dozens of confirmed cases.
Student to self-quarantine
An international student arriving in Auckland this morning planned to wear a face mask for the next 10 days.
The man, who didn't want to be named, arrived on the flight from Guangzhou.
He said while no one asked him to, he would try and quarantine himself.
"I'm pretty afraid, they argue about the people from China which is wearing the mask so I think I should keep it on.
"I'm going to stay at home."
If he did go out in public he will keep the mask on, he said.
The student said the flight was normal except for everyone wearing masks on the plane.
"The only have a temperature test at Guangzhou airport but it's like before boarding, it's not even before the security."
Prime Minister on the government response
Prime Minister Jacinda Ardern said cabinet would discuss the virus on Tuesday.
It would go through a process to ensure coronavirus was listed in New Zealand as a notifiable disease.
"That is not getting in the way of the response, it's just a more formal part of the process we need to go through."
She said the government made no apologies for the fact that "even though we do not have a case to date in New Zealand we are really rolling out everything we can including work at the border... We have taken the extra steps of putting health officials at the airport even though we don't have direct flights from (Wuhan)."
The Ministry of Foreign Affairs and Trade (MFAT) hadn't contacted Ardern about evacuating any New Zealanders from the Wuhan area, she said.
"That's something I'll talk to MFAT about."
MFAT said it was responding to four requests for consular assistance but had no plans for evacuations.
Sixteen New Zealanders are registered in Hubei Province, where Wuhan is the main city.
Asked about the National Party's criticism of the government's response to coronavirus, she said they were "doing what oppositions do".
This article was first published on Radio NZ.