But Dr Cunningham said in some cases, it is the GPs who have been reluctant to test due to mixed messages from health officials.
"Our goalposts kept changing as GPs - whether or not they've wanted us to swab, what's been funded, what hasn't been funded.
"On the GPs' behalves, there's been a bit of confusion. We just need clear guidelines and we will pick up the ball and run with it."
John Bonning from the Australasian College of Emergency Medicine said this is no time to be complacent.
"This is one of the key points we've got to get across, we have to be very very careful.
"What's happened in Melbourne, and possibly about to happen in New South Wales could happen here, if we take our eye off the ball."
He said while there is no vaccine, nor herd immunity, there must be a sustained surveillance programme.
Clear messaging from the Government is also essential.
"We want the public to know, actually it's not all over. We need to be swabbing people with any hint of illness, regardless of severity."
Doctors will be now surveyed about why patients are refusing to be swabbed and if there are other reasons why medical centres are not doing much testing.
The president of the Royal College of GPs, Samantha Murton, said the results will be given to the Health Ministry.
It will also ask what kind of capability and capacity practices have to do testing, she said.
The college is telling its members it is laying the groundwork for ramped up testing, Dr Murton said.
"We're looking at a strategy on how we can roll out an increase in testing and do that wisely, and make sure we aren't overwhelming practices that aren't capable or have no capacity."
Testing could be increased by next week, she said.
The ministry is urging people to say yes if their doctor suggests a Covid test and is assuring GPs the Government is covering the cost.
• If you have symptoms of the coronavirus, call the NZ Covid-19 Healthline on 0800 358 5453 (+64 9 358 5453 for international SIMs) or call your GP - don't show up at a medical centre