The 33-year-old was attacked in Doocot Park, Elgin, at around 1am on Friday.
She was not injured but was left shaken by the incident.
Police said they are following a positive line of inquiry regarding the suspect.
They issued a fresh appeal for people with information to get in contact.
Detective Inspector David Howieson said: "I would like to thank all those who have assisted with our investigation so far and would also continue to ask anyone with information which hasn't been provided to police yet to get in touch.
"Do you remember seeing or hearing anything unusual in the area around the time in question? Did you see a man going into or leaving Doocot Park?
"I would also continue to urge anyone with dashcam footage of the area and surrounding streets captured between 11pm on Thursday and 1.30am on Friday to get in touch as soon as possible.
"A man we would like to speak to is aged in his twenties, of a slim build, around 5ft 7in to 6ft and was wearing a black hooded top.
"He was last seen walking into Doocot Park."
Mr Howieson added: "Incidents of this nature are extremely rare so I can understand the concern local residents have.
"Please be assured that every effort is being made to identify the person responsible."
Extra patrols have been carried out in the area.