The man, who is suspected of attempting to rape the girl, is described by police as elderly. He was alone with the girl in the stairway, but was interrupted and fled.
Witnesses say he ran towards a small wood by the Björndammen residential area. The attack took place at around 12:50 pm on Thursday.
Police have not released any details of who the witnesses were or whether they saw him with the girl. It has not been revealed whether the girl sustained physical injuries.