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Some district health boards were starting to advise people to go back to their general practitioners for Covid-19 swabbing.
The Ministry of Health said each DHB would be making its own decision on how best to provide testing over the coming weeks.
"This may involve a mix of CBACs, mobile services, primary care and other community-based testing.
"DHBs and PHUs [public health units] have done significant testing over the last few weeks and we are very pleased with the surveillance data that shows the Covid-19 prevalence in all New Zealand population groups is now extremely low."
The ministry has told DHBs to ensure there was equitable access to testing for those who have symptoms consistent with Covid-19.
The number of people being tested for the virus would likely drop as the focus moves from asymptomatic people to largely testing symptomatic people, the ministry said.
"If we were to see increases in cases, then we would reconsider our testing approach."
The ministry was still finalising its sentinel and surveillance testing strategy and it will be considered by Cabinet next week.
GPs are hoping that when that strategy is finalised the test remains free of charge.
College of GPs Medical Director Dr Bryan Betty said they expected to take over the majority of testing in the next couple of weeks as the case definition changes.
"At the moment Covid testing is free, we expect that situation to continue if the patient fits what we call the case definition.
"[It] certainly wouldn't be free if the patient just requested a test because they wanted one. We generally wouldn't do that. So it needs to fit the priorities the government puts in place."
If testing came with a cost that would create a financial barrier and create inequities, Dr Betty said.
"There shouldn't be a financial barrier to being tested and we'd expect that to be the case going forward."
The upside to testing returning to general practices was that it would allow doctors to take a more holistic approach to a patient's health when they presented for testing.
"That's the role of the general practitioner is to provide that overall clinical overview of a patient's health.
"So it may not just be the Covid swabbing, if it's a sore throat, and there's potential for it to be strep that may need to be dealt with - there's often a cluster of other problems that need to be dealt with."
District Health Boards said they would be able to upscale testing quickly if they needed to.
CBACs by DHB
- Waikato DHB had reduced down to just one testing station in Hamilton.
- In Whanganui, the CBAC at the hospital would continue running, but the five other stations in Marton, Bulls, Raetihi and Taihape were closed with the local GPs and medical centres taking over assessments and swabbing.
- Mid-Central was reviewing the CBACs and testing sites and was planning how testing would be carried out at different Covid-19 levels.
- Auckland and Wellington were still operating at full capacity for now.
- Across Christchurch and the West Coast there would be reduced stations from next week.
- The Queenstown CBAC was closed on 11 May, but others were still operating in Dunedin and Invercargill.