"The children concerned have generally been walking alone. They have been approached in the vicinity of primary and intermediate schools [but] not necessarily directly outside the school grounds," Mr Van Den Broek said.
"Attempts have been made to coax children into the vehicles using the offer of money or lollies but also some children have been threatened with physical violence."
He said any suspicious activity should be reported to police by calling 111.
"Perhaps the most important way parents can protect their children is to teach them to be wary of potentially dangerous situations."
It was also important to teach children they could say no to an adult.
"You should also talk to your children about how they should handle dangerous situations. One way is to teach them 'no, go, yell, tell'.
"If in a dangerous situation, kids should say no, run away, yell as loud as they can and tell a trusted adult what happened right away."
Rotorua mum Katrina Heywood said she was told about the stranger-danger incidents on Wednesday at an after-school programme.
"With my own children, I make sure they know that only me, my parents or my partner can collect them."
Ms Heywood said she had heard of one child using a password which their parents gave them.
She said if someone in a vehicle asked to take them for a drive and did not mention the password the child knew to walk away.
Rotorua Principals' Association president Deborah Epp said Rotorua schools had been informed and were passing on the warning to parents.
At Mokoia Intermediate they taught students about stranger danger as part of their health programme, she said.