The Ministry of Health said the tests were mainly precautionary and not necessarily suspected cases of coronavirus.
A total of 122 tests have been done across three laboratories In Auckland, Christchurch and Wellington.
All have returned negative results.
Health officials have urged people to get winter flu vaccines this year. The Ministry of Health said the flu shot would not stop people getting Covid-19, but it would help prevent them getting seriously ill.
Director of public health Caroline McElnay said it would not be easy dealing with cases of the new disease and the flu season at the same time.
"That would be a challenge and we acknowledge that as a challenge," she said.
"What we can do with flu season is make sure that as many people as possible get vaccinated with the flu vaccination and that at least will hopefully reduce the impact that we have from flu."
She said any Covid-19 vaccine was probably about 18 months away.
The Ministry of Health said it was working hard to ensure frontline health staff around the country had the equipment needed to respond to an outbreak.
The assurances follow cries from the College of GPs saying many clinics had run out of protective gear like masks.
Dr McElnay said the ministry would get resources from overseas if needed.
"That's part of the assessment, it's making sure what we've got in country is well distributed but also what do we need to get in to New Zealand so that then we can keep the supply chain going.
"We are ensuring that supplies of equipment that they need will get to those practices as soon as possible."
Dr McElnay could not say exactly where the gaps were.
Finance Minister Grant Robertson today said he was assessing whether to include extra stimulus in this year's budget to soften the blow of the virus.
The government is preparing for no GDP growth in the first half of this year. Whether the economy will bounce back in the second half of the year will depend on the long-term effects of the virus.
Robertson said now was the time of year that the Budget was starting to be put together.
"It's a difficult job to do with so much uncertainty around, but clearly that's something that we're thinking about.
"Bear in mind we have an expansionary fiscal policy and obviously we had the big infrastructure investment that we announced recently that will provide ongoing stimulus in to the economy. But clearly we have to look at a longer-lasting outbreak and the fiscal response that will be needed.
"The Budget will be a time to talk about that."