Hamilton police said they had an idea of who the man might be.
"Police would like to hear from anyone who may know this man or who may have seen a silver car in the area.
"Police are also working to establish if there are any links between yesterday's incident at Te Pahu and other similar incidents that have occurred in the past month."
The inquiry was in the early stages and all avenues were being explored.
A local told the publication: "He parked his car right next to our school field jumped the wooden fence. He was carrying a hammer. He ran up to girl who was playing, she ran away as fast as she could and got away.
"He returned to his car, stood by his car for a while staring at the kids, then he put the hammer in his boot, got back in his car and drove off."
She said teachers reacted quickly, placing the school in lockdown.
"But when is too late too late? We have a pre-school up the road with kids freely playing by the fence line. I'm terrified."
