The teenagers were walking along Lower Hanham Road when the occupants of a silver car, possibly a VW Golf or Polo, wound down the window and called out to them.
When the teenagers ignored them and walked on, one of the men held up a mobile phone as if he was taking a photo. At no point did either of the men leave the car, neither did the girls approach the vehicle.
They told their family about the incident when they got home and it was reported to police via the school the following Monday.
Today Neighbourhood Sergeant Adrian Fallows said: “The girls did the right thing by walking away and telling someone, although we’d always encourage people to report a suspicious incident like this straight away by calling 101. Although no offences were committed, I would like to reassure the community that we are looking into this.
“We’re keen to speak to the two men, described as being in their 20s with dark hair. Anyone with information which could help is asked to get in touch through our website, www.avonandsomerset.police.uk/contact, or by calling 101, quoting reference 5217109373.”
Police advice is for children to avoid wearing headphones so they can be aware of their surroundings and to walk facing the traffic.
If they are alarmed or frightened by a stranger, they should run home or to the nearest busy public place, such as a shop, and tell someone straight away.