The children, aged 12 and 10, were approached by two men driving a silver van on Half Crown Way, a quiet residential street, at around 5pm yesterday (Monday).
The girls managed to escape and were left shaken but unhurt. A local resident contacted police.
Two men, aged 46 and 17, were later arrested in Bradford.
Detective Sergeant Paul Schofield who is investigating, said: “I understand news of this incident will send shockwaves through the local community, but I hope the quick arrests of two men will go some way to reassure that we are treating this incident seriously, and we will carry out a thorough investigation into the incident.
“I would like to praise the girls for their quick thinking which not only got them away from the scene but also provided officers with information vital to this investigation.
“I would also like to thank the local residents who came to the aid of the girls following the incident and contacted police.”
A 19-year-old man and a 46-year-old man were arrested a short time later in Bradford on suspicion of attempted kidnap. They remain in police custody at this time.
Anyone with information on this incident is urged to contact North Yorkshire Police on 101 quoting reference 12190044299. Alternatively information can be passed to the independent charity Crimestoppers anonymously 0800 555 111.