The children were playing in woodland on Friday 13th around 6pm in Perth when they were reportedly approached by a teenager, who is described as being 'thin with pale skin and dark circles under his eyes', with a long fringe with purple highlights.
The pair, a girl aged nine and a boy aged 13, told police that the man,who was dressed in a black hoodie, then made threatening comments.
The teen then left the scene leaving the children so frightened that they dialled 999.
Constable Neil Aitkenhead from Perth Police Station said: "While none of the children were injured during this incident, they were left understandably distressed.
"We are keen to trace the suspect as soon as possible and anyone who recognises him is urged to contact police immediately.
"Likewise, anyone with any further information relevant to our ongoing investigation should also get in touch."
• Those with information can contact Perth Police Station via 101 and quote incident number 3461 of the 13th September. Alternatively, an anonymous report can be made to the charity Crimestoppers on 0800 555 111.