But they acknowledged there was a problem in New Zealand because children did not have the cognitive skills to ride on the road until 10 years old.
"There is a period of approximately six years during which most children cannot ride legally on the footpath or safely on the road.
"This poses significant challenges as the government works towards making urban cycling a safe and more attractive transport choice."
They added: "At the same time, it is important to recognise that footpaths are, first and foremost, the domain of pedestrians."
New Zealand appeared to be unique in restricting footpath cycling based on wheel sizes, transport officials said.
The policy is a relic from road rules which were mostly overhauled 30 years ago.
The ministry and NZTA said most Western countries limited cycling on footpaths by age and others banned it altogether. In Australia, some states allowed cyclists up to 12 years old to use footpaths and other states allowed all ages to use footpaths.
Many young people rode on the footpath illegally in New Zealand because they did not have the ability or awareness to use the road, transport officials said.
Yet the risk of fatal crashes on footpaths were "extremely low" and serious injuries were uncommon.
In the 10 years to 2015, 1065 cycle crashes, or 10 per cent, took place on footpaths.
Of those, 14 crashes involved a pedestrian, seven resulted in serious injury, and two were fatal - though both cases involved an out-of-control car.
Over the same period, 90 cyclists died on the roads, a quarter of them under 20 years old.
The ministry and NZTA said any law change would have to be accompanied by education campaigns and training for kids.
Cycle skills trainers are currently unable to teach children about footpath cycling because it is an illegal activity.