The poll found that only 10 percent of Norwegians found the use of tracking devices unacceptable, while 60 percent were in favour.
GPS tracking watches for children allow parents to see the exact location of their child throughout the day, sending out an alert warning parents if they leave a set area, and, in some cases, even allowing parents to eavesdrop on conversations.
The Norwegian Data Protection Authority (NDPA) is worried that the new devices could be an invasion of children's right to privacy.
"It is an important principle, that you should be able to move around freely without being monitored. Privacy is important for children as well, " NDPA head Bjørn Erik Thon told Norway's Aftenposten newspaper.
"It's about being allowed to develop ones own personality without being observed and controlled all of the time. I am worried that children's ideas of privacy will be affected if they are tracked. Children should be allowed to have secret places where they can go, without their parents knowing where they are all of the time."
Norway's children's ombudsman told the newspaper that the new devices and apps were a legal grey zone in Norway, and clearly violated the UN convention on the rights of the child.
"It is clearly written that children have a right to privacy.They should not be monitored in this way," Anne Lindboe told Aftenposten. "We can not let technical gadgets take over parents' efforts. There are some challenges life presents, that children must face. If children are tracked and monitored, parents regulate their children's lives."
Electronic tracking of children's activity has become increasingly popular, with devices such as the HereO, Tinitell, and FILip2 all launching in the last few years, and an array of apps for sale which track what children and teenagers do online.
There are also GPS trackers on phones that are sometimes hidden so that the person using the phone is unaware that they are being tracked.