Greens Party health spokesman Kevin Hague told Radio New Zealand the Government had not thought about how it was going to implement its policy.
"And when they finally did come round to that, they elected a policy setting that meant actually one in ten injured kids would not in fact get that free visit," he said.
The money that was being saved was "peanuts", Mr Hague said.
"The Government is just scrimping and displaying a stingy attitude and its kids who are paying for it."
Labour leader Andrew Little told RNZ the Government promised free doctors visits for all under 13s and it should deliver.
'It shouldn't matter whether you go there (to the doctor) for an illness or disease or as a result of an accident either way the promise is for free doctors visits and that's what should happen."
In a statement Ms Kaye said about 213,000 children would receive free injury-related doctors visits.
Some GPs chose to charge patients a fee and that those doctors were typically in higher socio-economic areas, she said.
Health Minister Jonathan Coleman said the Green Party had got it wrong on the doctor visits.
"We expect levels of uptake by general practices of the free under 13s scheme to be similar to uptake of the under 6s scheme," he said.
"Currently 98 per cent of general practices offer free doctors' visits for under 6s. Initial uptake was 70 per cent in January 2008, and it has steadily increased to current levels."
There were only about 12 general practices in New Zealand that were not offering free under 6s doctor visits, he said.
Ms Kaye said following consultation, ACC's additional contribution to GPs to encourage them to provide free visits for under 13s was increased to $27.5 million over three years.
"Similar to the general practice uptake of the under 6s scheme, we expect the number of GPs providing free injury-related visits to steadily increase over time," says Ms Kaye.
"We want as many children as possible to access free visits, and that's what the scheme will help deliver.
"More than 400,000 primary school-aged children and their families are expected to benefit from the Government's investment in free under 13s," Ms Kaye said.