Two children - aged 8 and 10 - were approached by a man in Merlin St, Dunedin, on Wednesday morning, Senior Sergeant Mel Aitken said.
The man was described as a European aged between 30 and 40, of thin build, with short black hair.
He was wearing a T-shirt, and a pair of Rio skin-coloured underwear.
The man was driving an older dark-coloured 4WD or van.
The children were not harmed in the incident and were able to alert authorities.
Snr Sgt Aitken said parents should remind their children what to do in such situations: such as scream or attract the attention of other adults.
"Alert an adult, and don't panic."
In another incident, a man is reported to have followed and called out to schoolchildren in Portobello.
Senior Constable Lox Kellas said a girl reported being followed by a man, described as an unshaven olive-skinned European in his mid-30s, who was wearing a beanie.
Other children saw a man fitting this description in the Portobello Cemetery. He was holding a silver object in his hand and is reported to have called out to one of the children.
Police also fielded a complaint of a man fitting the same description loitering near Abbotsford School on Wednesday and Thursday afternoons.
Snr Sgt Aitken warned parents to be vigilant when dropping off or picking up their children, and to report any suspicious behaviour.
Police had increased patrols around city schools.
• Copper telephone wire from Anderson's Exchange Pharmacy, on Broadway, was removed on Thursday, Snr Sgt Aitken said.
The theft left the pharmacy temporarily without telephone communications.
