Mr Bowman said police were yet to interview the young woman, who was "very shaken" by the ordeal.
"This is the latest of a number of reported incidents which have involved an elderly male in a white van approaching young children over the past month."
He said clearly police wanted to identify who the man was and were asking the public who might have been in the area about the time of the incident and had seen the white van or the man approach the young woman to urgently contact them.
"If you see a suspicious vehicle in particular a white van with an elderly male driving it in your area please take the registration number and ring the police at the time."
Invercargill police also investigated two serious assaults, in which five people were injured yesterday.
About 12.20am police attended an incident outside a Nelson Street property were a 50-year-old man was alleged to have assaulted two males and two females with a weapon, Mr Bowman said.
The victims were treated at the Southland Hospital with moderate to serious injuries.
All have since been discharged from the hospital.
Mr Bowman said a team of detectives from the Invercargill Criminal Investigation Unit spent yesterday speaking to a number of witnesses and victims and completing a scene examination.
A 50-year-old man was arrested at the scene at the time of the incident and will face a raft of serious assault charges when he appears in the Invercargill District Court today.
And, about 8.30am yesterday, police were called to a stabbing at an Earn Street address.
A 36-year-old man was hospitalised with moderate head injuries and was later discharged, Mr Bowman said.
A 24-year-old man who was known to the victim has been arrested and will also appear in the Invercargill District Court today on assault charges with more serious charges possible following further inquiries.