Some GPs are now saying they won't accept walk-in patients with any flu-like symptoms, as they expand their coronavirus precautions.
Five New Zealanders have tested positive for the virus, with two more likely to have had it, but health authorites are preparing for a possible rise in numbers.
Most GPs had already been telling patients who suspected they could have coronavirus not to visit their clinics.
But some are now widening their restrictions to any kind of flu symptoms.
The College of GPs president Samantha Murton said they were preparing for the potential transmission of Covid-19 in the community.
If that happens, there may be people who don't know they have the disease who turn up to clinics and unknowingly spread it.
"At some stage we'll be moving into a phase where there may be community transmission, as has happened in other parts of the globe, so this is a step to prepare ourselves so that people get used to it and are careful," Dr Murton said.
"We're trying to make it as very clear as possible that you can be spreading virus, and it may not be Covid, but you can be spreading the virus and if it happens to be Covid then that's a serious thing for the rest of the practice and other patients."
The Ministry of Health's Director-General of Health, Ashley Bloomfield, said people should not go to work or public places if they were sick, and this was particularly important for large gatherings like concerts.
"This is the time when we've got to be much, much more strict with ourselves," Dr Bloomfield said.
The World Health Organisation declared overnight that Covid-19 is now a global pandemic.
Tedros Adhanom Ghebreyesus, who heads the UN agency, said the WHO is "deeply concerned by the alarming levels of spread and severity" of the outbreak.
He also expressed concern about "the alarming levels of inaction".
"We have, therefore, made the assessment that Covid-19 can be characterised as a pandemic," he said at a briefing in Geneva.