From this week, under-6s in the Southern district have access to free after-hours care, but that does not mean every practice is participating.
Mornington Health Centre practice manager Barbara Bridger said it would not sign up to the scheme until it was satisfied it could cope with extra demand.
It would be "remiss" to do so at present, because of the risk to patient safety, she said.
"We believe we need more time to consider the proposal and put practices in place to ensure patient safety."
The medical centre would have to provide free appointments after-hours for under-6s, regardless of whether the child was enrolled with the practice.
This could see a big increase in demand, which had not been quantified, she said.
Ms Bridger said a planned telephone triage system designed to help parents decide if their children's health needs were urgent was not yet in place.
She had concerns that telephone triage was not an appropriate way to assess children's health needs.
Dunedin Urgent Doctors and Accident Centre manager Martin Chamberlain said the centre had signed up to the initiative.
It would probably increase demand, and would be monitored.
The issue was different for urgent doctors, who were used to treating patients from anywhere.
Queenstown Medical Centre chief operating officer Shane Zeederberg said he expected the entitlement would increase demand, but the practice was ready to deal with it.
Southern District Health Board chief executive Carole Heatly, in a press release, said an agreement with the Southern Primary Health Organisation would see free after-hours care for under-6s available throughout the district.
In their joint press release, Southern PHO chief executive Ian Macara said parents should recognise the service was for urgent health needs, rather than as a substitute for normal visits to the family doctor.
In response to a question about how many practices had signed, Mr Macara said by email:
"We have agreed to provide coverage throughout the district from next week..
"We are now working with practices to determine the finer details of that coverage."
The Otago Daily Times was unable to ascertain how many practices had signed.
New Zealand First health spokeswoman Barbara Stewart said implementation of the scheme was "a mess".
Uncertainty about which practices were providing the free care could endanger child health, she said.
In Parliament on Thursday, in response to a question, Health Minister Tony Ryall said "excellent progress" was being made signing practices.
"We have to remember, though, that this is not a compulsory scheme.
"We have had to negotiate this with individual after-hours centres and general practitioner networks."
More than 90% of New Zealand children aged under-6 had access to free after-hours GP visits, Mr Ryall said in a press release yesterday.
The Government has allocated $28 million over four years for the initiative.
