Bloomfield said the Ministry of Health was expecting sporadic cases of Covid-19 to appear across New Zealand.
There have been 155 tests, one of which has returned positive, and there are currently 31 tests underway.
"There is constantly a number of tests underway, we would only provide additional detail if any returned a positive result," Bloomfield said.
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Bloomfield said officials were strengthening the response at New Zealand's borders, with an increased presence of health staff at airports.
The six people in quarantine at Whangaparaoa remain well. Yesterday two other people were reported to be showing signs of the virus.
Anyone who has symptoms and has been to a country where Covid-19 is present should not go to the emergency department or your GP without calling ahead, Bloomfield said.
They should call Healthline, their doctor's clinic or the hospital first, he said.
There have been over 1600 calls to Healthline.
Dr Michelle Balm, clinical leader for infection services at Capital & Coast DHB said there has been no rationing of tests for Covid-19.
There have been no cases in the Wellington region, she said, so the DHB has been focused on early detection.
If a patient came to hospital or their GP with a suspected case of coronavirus they would be assessed on a risk basis focused on their symptoms and where they have travelled.
Rumours had been circulating, Balm said, that doctors were rationing tests. Balm said this is not true and New Zealand has capacity for hundreds of tests per day.
ESR and several large laboratories across the country are handling the tests and can receive up to 1000 every day.
"Nobody wants to miss the first Covid-19 case within the region," she said.
However, Balm said there is a risk with false negative results from the tests.
"We know that it is not a good idea to test asymptomatic people at present, it is likely to give a false sense of security.
"We know that the test reliably performs in people who have symptoms."
She encouraged anyone who suspected they had the virus to call Healthline before going to see a doctor.
"If you are worried you have Covid-19 it is a good idea not to front up without prior arrangement with an emergency department or your primary care provider," Balm said.
Two NZ cases had shown coronavirus symptoms
Bloomfield had said yesterday that there were two people in New Zealand with symptoms consistent with Covid-19.
They had arrived on a different flight to the first case of Covid-19 in New Zealand, a person in their 60s who had arrived from Tehran via Bali on Emirates flight EK450 on February 26.
That person was feeling unwell when they flew into New Zealand and they and their family wore masks on their flight, and they were admitted to Auckland City Hospital not long after arrival. They are in a stable condition and are recovering well, Bloomfield said.
Passengers who sat close to the person on the flight have been contacted. Bloomfield said nobody sitting near the person had been tested for Covid-19 as none of them were showing symptoms of the disease.
However two people who were on the flight are being monitored in Nelson for symptoms of the virus and are in self-quarantine.
There was still no sign of "community transmission" in New Zealand, Bloomfield said.
After their diagnosis, the Ministry of Health said it was confident the swift actions of the person and their family, and the health sector, meant there was a low risk of the virus spreading in the community from that case.
New Zealand does not have Covid-19 circulating, the MoH says on its website.
"We knew the likelihood of an imported case in New Zealand was high, however, the likelihood of a widespread outbreak is low-moderate."
The Government yesterday extended the travel ban on foreigners arriving from China and Iran by another week, until March 10, while those arriving from northern Italy or South Korea are asked to self-isolate for 14 days.
Worldwide there have been more than 90,000 confirmed cases, with more than 3000 deaths - mostly in mainland China. Nearly 46,000 people are reported to have recovered from the virus.
