"We are appealing for him to contact us, or for anyone who knows his whereabouts to pass that information on to police.''
Police have described the alleged offender as a solidly built Caucasian, aged in his 20s, about 1.7m tall. He was clean-shaven with dark hair and dark complexion.
The man was reported to be wearing a cap, a white hoodie with a grey triangular pattern and maroon jeans.
Timaru police said they were continuing to appeal for information from anyone who was around Sir Basil Arthur Park between 7.45pm and 8.20pm on Tuesday, or who had information about the incident.
The girl had been riding her bike on State Highway 8 near the park when she was allegedly approached by the man.
A short time later he dragged her off her bike, across a fence and into an area of bush, Ms Neill said.
A witness from a nearby property went to help her and the assailant ran away. A police dog team was unable to find him.