The boys, who were playing out on their bikes, said they were approached by two men who remained inside the car while two others asked about accommodation at a nearby caravan park.
The incident occurred near the Flask pub, off the A171 Whitby to Scarborough road, between 4.30pm and 4.48pm last Sunday.
The boys told police that the men, whom they described as “Asian” and aged in their 20s to 30s, encouraged them towards the car with a view to haing their photographs taken. One of the men, who was wearing a red coat, allegedly put his arm around one of the boys.
It was at this point that the youngsters rode off and reported the incident to their parents, who alerted police immediately.
The four men drove off in the direction of Whitby, kin their navy blue Audi A4 Tdi saloon.
CCTV pictures have been released of the two men who enquired about the accommodation to assist this effort.
PC Michael Jamalizadeh, from Whitby Police, said: “This incident is clearly a cause for concern and we are doing everything we can to investigate the circumstances, trace the men and car involved, and provide reassurance in the local community.
“If there is an innocent explanation about what occurred, then it is vital that the four men in the navy blue Audi A4 saloon car come forward without delay.
“I also urge anyone with information that could assist our enquiries to contact the police or Crimestoppers as soon as possible.”
Anyone with information should call 101, or Crimestoppers, anonymously, on 0800 555111.