The girls, aged between eight and 11, were walking along on Wedderburn Avenue near Wedderburn Close when a man in front of them held his arms out, blocked their path and said something along the lines of “give us a cuddle”.
Alarmed, the girls turned around and ran home, and they ran away, the man shouted after them.
The man was believed to be aged in his late 30s, was around 5ft 5ins tall, of medium build with black hair and he wore a khaki-coloured hooded top and jeans.
A spokesman for North Yorkshire Police said: “If the man responsible for the incident reads this appeal, we urge him to come forward and explain his actions.
“The girls were very shaken by what happened, and did the right thing by running home and telling their parents.”
Police urged anyone who recognises the man from the description or who witnessed the incident, which happened at around 4.40pm on Friday, to call them on 101, quoting reference number 12180002776.