The incident took place on the Faverdale Black Path on Sunday (January 5) when a woman was walking home along the upper part of the path near Minors Crescent.
The woman – who was left uninjured but shaken – was threatened by a man with a knife who demanded money from her at around 5.50pm.
After she refused to hand anything over, the suspect, who is described as a young man wearing a grey tracksuit, ran off down the steps to the lower path and out of sight.
Durham Constabulary has today (January 8) confirmed that the investigation remains ongoing.
It is not yet known whether the suspect has been identified, or if any arrests have been made.
Officers still want to speak to anyone who may have information on the incident.
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The suspect has also been described as wearing a dark mask around the bottom of his face with his hood up, and was carrying a Sainsbury’s carrier bag.
If you have information, call the force on 101 with any information, quoting crime reference number CRI00590520.
Information can also be passed on anonymously to Crimestoppers on 0800 555 111.