Hundreds of doctors have had patients refuse to be tested for Covid-19.
The College of GPs surveyed 800 members about their experience with testing and half of them said they had patients decline a test when one was recommended.
Reasons included not wanting to put children through the discomfort or not thinking one was necessary.
The college's president Samantha Murton said doctors were fighting complacency from people used to living in places free from the virus.
Testing was an important part of the strategy to keep Covid-19 from taking hold again by making sure it was not spreading in the community.
"If we're offering a test it's not because we're doing it for fun, it's because we want to make sure nothing is happening," Murton said.
Rates were increasing again after a drop off over the past few weeks but were not yet at the goal of about 4000 a day.
People needed to listen to the advice of their doctors and play their part, Murton said.
They could have an insight patients are not aware of - like a sudden local spike in coughs and colds, or an influx of overseas arrivals, she said.
"If there is a breach and we don't know about it then it can cause trouble quite quickly without us being aware of it until it has got out of hand. So, it is a matter of us all being vigilant."
Doctors told the college they were keen to take part in a surveillance testing programme but they wanted clear direction from the Ministry of Health about it.
As well as borders, a key surveillance focus should be cities with isolation hotels, Murton said.
The ministry said it was working with both GPs and emergency doctors to encourage them to test anyone who turned up with symptoms.