Director-General of Health Ashley Bloomfield said there were two more cases in New Zealand that had symptoms that might be consistent with Covid-19 coronavirus.
They were not on the Emirates flight that the patient who tested positive was on.
He said he did not know where those two suspected cases were in New Zealand.
There was still only one positive case in New Zealand so far.
The results of the two suspected cases may have been tested today, in which case the results should be available now, but Bloomfield said he did not know if they were tested today; the media would be notified if there were any more positive cases.
He said the two people had the "travel history" and symptoms that might be Covid-19.
PM extends coronavirus travel restrictions
Cabinet has extended travel restrictions in response to the corovonavirus outbreak.
Prime Minister Jacinda Ardern said border management was the first line of defence and travel restrictions would be extended for Iran, China and for passengers on the cruise ship the Diamond Princess, that was docked in Japan for seven days.
People coming into New Zealand from northern Italy and South Korea would need to self-isolate for 14 days, she said.
People coming from those areas would need to complete a form to enable health officials to contact those individuals to ensure they are in self-quarantine, and what is expected of them.
Ardern thanked the health professionals that have been part of the response to the Covid-19 coronavirus.
Eight thousand people had been helped with self-isolation so far.
There were robust measures in place to deal with Covid-19, she said.
The patient with Covid-19, NZ's first confirmed case of coronavirus, is stable and improving and officials had traced the 15 at-risk passengers who shared the same flight.
This was originally thought to be 18 people, but has been reduced.
"We have 87,000 cases globally. The vast majority still remain in China. We have 7300 outside mainland China," Ardern said.
"We know self-isolation works."
Healthline had reported over-compliance, not non-compliance with self-isolation, she said.
Ardern said a special Covid-19 Cabinet sub committee had been set up.
Cabinet has decided to expand the regional business partner programme to protect jobs affected by Covid-19.
Ardern said the programme - which already has $15.2m - would see an extra $4 million.
The programme supports a focus on firms in the regions with issues such as cash flow and the ability to pay taxes.
Ministry of Social Development teams were also on the ground, meeting employers and assisting people at risk of losing their current jobs at a regional level.
Those teams will coordinate with other employers to transition people into different jobs, such as forestry workers doing wilding pines work.
The economic response was focused on job losses, she said.
She and Finance Minister Grant Robertson were also meeting with business representatives and the Council of Trade Unions this evening.
"In the meantime, public health remains our primary focus."
Ardern said on the east coast, as many as 300 individuals have been affected by at least a reduction of work hours.
It was too early to say how widespread those effects will be, she said.
All but 10 passengers on the same Emirates flight as the patient who has tested positive for Covid-19 coronavirus have been contacted, she said.
Those 10 who had yet to be contacted were not in close proximity with the patient, and contacting everyone on that flight was a precaution.
Ardern said people coming to New Zealand from northern Italy for a holiday may rethink their travel plans because they would need to self-isolate and be stationary for 14 days.
Ardern said the patient's mobility issues that were reported were not related to the coronavirus.
Ardern said, as of today, there will be verbal announcements for all people coming in on international flights, regardless of where they are coming from, and everyone will be told about health warnings in person except for E-gate passengers from USA and Australia.
The virus has spread to many parts of the world, including major outbreaks in South Korea and northern Italy, from where people are not currently restricted from travelling to New Zealand.
There is currently one patient, who recently travelled to Iran, being treated for coronavirus at Auckland Hospital, and 11 Covid-19 tests currently awaiting results.
Today Nelson-Marlborough Health confirmed that two people in the region are being monitored for signs of Covid-19.
A health board spokesperson said the two were passengers on the same Emirates flight - from Dubai to Auckland, via Bali - as the person who has tested positive for the virus.
The two people in the Nelson-Marlborough region were now in isolation and were being monitored daily by health services, but neither had been tested.
This morning Ardern told Newstalk ZB that the announcement to extend the travel ban to Iran came just before the first New Zealand case was confirmed.
"We did know we had a potential case, but at that point there were still negative tests coming through."
Ardern said travel to countries with a high number of cases - such as Italy and South Korea - was still open at this stage, but would be monitored as the level of infection was still unknown.
"We make judgements based on scale - whether or not we believe we've got a true sense of transmission - the health system in place, the border controls and border measures that are being in used, both within in the country and in transit to New Zealand."
Ardern said the public should follow basic hygiene practises, and the Government would be closely monitoring whether more-specific measures were necessary.
"[There] might not be a reason for a complete ban for travel from those countries, but what about being regionally specific and saying 'if you have come from that region, self isolate'?"
The Government announced a travel ban on foreign nationals travelling from mainland China since February 2.
The first New Zealand Covid-19 case was announced on Friday, sparking a flurry of people buying emergency items at supermarkets with reported queues running out the door.
On Saturday, Ardern called out the media on their coronavirus reporting and said she took particular exception to the headlines.
"I do appreciate that not all journalists write their own headlines, but now is the time for factual information and giving the public as much factual information as possible.
"Those headlines did a disservice to the media in New Zealand and also the public."