The girls, who are aged five and 15, were walking in Shore Road, Sandbank, in Dunoon when a man sitting in a car called them over and asked them for directions.
When they reached the car, the older girl noticed the man was carrying out an indecent act. Both the girls then ran away.
The man is described as white and in his mid 50s with a dishevelled appearance. He had thinning grey hair with grey stubble and unkempt eyebrows, and had prominent white straight teeth. Although he had a gaunt face, he was of stocky build.
He was wearing a mustard coloured T-shirt with white writing and circles across it.
He was in is a three-door silver coloured Vauxhall with dark tinted windows at the rear.
Detective Inspector Douglas Wilson said: "This is quite frankly disgusting behaviour and it was a very upsetting experience for these children.
"It is not believed that this incident is linked to any others in the area. However we are stepping up police patrols to offer extra reassurance."