Prime Minister Jacinda Ardern said 53 New Zealanders are registered to be in Wuhan - the city at the epicenter of the deadly coronavirus outbreak.
The Government has also decided that coronavirus is now considered a "notifiable disease" - which gives officials powers to quarantine people if required.
Ardern told media at her post-Cabinet press conference that 20 Kiwis in Wuhan have contacted New Zealand, seeking consular assistance.
But she said Ministry of Foreign Affairs and Trade is not aware of any New Zealanders in the city who are showing symptoms.
Ardern said she will be talking with Australian Prime Minister Scott Morrison soon.
When it comes to testing, Bloomfield said any tests are being sent to a lab in Melbourne but testing in New Zealand will be available later in the week.
He said health advice around people going to Chinese New Year celebrations is currently being prepared.
Bloomfield said it was impossible to tell when the virus will come to New Zealand – he said yesterday it was "likely" New Zealand will get a case.
Earlier National called for the Government to follow the lead of Japan and the US and evacuate all New Zealand citizens from Wuhan in China – ground zero for the recent outbreak of coronavirus.
"The feeling is that we're going to die in China. We need to get out of here," he told the Herald earlier today.
He estimated the family had only a few days' worth of food left, with all they have going to their daughter, Taylor.
Ardern yesterday said she was seeking advice from the Ministry of Foreign Affairs and Trade (MFAT) regarding the evacuation of New Zealanders, such as Aaron and Taylor, from Wuhan.
But National Leader Simon Bridges said Ardern and the Government need to stop sitting on their hands and act now to bring New Zealanders home.
"A responsible government would be looking after its people. Countries around the world are evacuating their citizens and putting them in quarantine for 14 days," he said this morning.
"We have a desperate family telling the media they fear they'll die of the virus or die of starvation. The Government needs to act to protect them."
So far, close to 80 people have died, with a further 3000 inflected with coronavirus.
The governments of Japan and the US have begun evacuating their citizens from the region.
France has confirmed their citizens will be evacuated by midweek, while Russia, Spain, Sri Lanka and Thailand are asking China to allow their nationals to leave.
Several other countries, including Australia and the UK, are also considering evacuation options.