The girls were approached on Albert Road and Queens Road in Keynsham on Saturday morning (3rd August).
The man is described as Afro-Caribbean and in his 20s or 30s, with a Jamaican accent. He wore a bandana and may have had a Jamaican basketball top on.
Avon & Somerset police say that several people have provided them with details about a J-registration convertible VW Golf being driven by an Asian man. They say they are satisfied that the vehicle and its owner has nothing to do with these incidents and they have been eliminated from inquiries.
Writing on the force’s Facebook page, a spokesman said: “Our inquiries into these incidents continue and there is no need for undue alarm. However, as always please remember common sense as you go out and about. If it is late stick to well-lit areas, walk with people you know and trust and if someone makes you feel uncomfortable cross the road and walk on the other side.
“Finally always let people know where you will be and what time you will be back.
“We don’t know what this man wanted but we would like to speak to him. If you have information about these incidents please call us on 101.”