Rumours began to circulate on social media after the incident in the Tesco store at Catterick Garrison on Saturday afternoon.
Comments suggested a group of men of Middle Eastern appearance had chased the girls into the supermarket, but North Yorkshire Police say this is a 'distorted' version of events.
A police statement read:
"Police have spoken to all parties involved and have viewed clear CCTV footage. This CCTV supports a version of events where the group of men were shopping in Tesco when the girls approached them and began taking photos of them. The men asked them to stop taking the photos and to delete them, then security staff quickly intervened. Officers are aware of what could be described as inflammatory comments on social media, and have reiterated that the incident is not as reported. They are appealing to members of the public to stay calm and to think carefully and not post any racist, inflammatory material online."