Detectives in north Belfast are investigating reports two young girls were approached by men.
The PSNI called for calm after police were told of two separate incidents within 10 hours of each other.
"The public can be assured that officers are investigating these reports and inquiries are continuing," a PSNI spokesman said.
Police said it was reported that a 10-year old girl was walking on Spamount Street at 8.30am on Friday when a man in a white van offered her sweets and swore at her, at which point she ran off.
At no stage did the man attempt to get the girl into the van, they added
The man is described as having scruffy black hair and a black beard, wearing a blue jacket and dark khaki-style trousers.
In a separate incident shortly after 6pm on Friday, it was reported that a 13-year-old girl was walking on Kilcoole Park when a dark blue Ford car slowed down beside her before stopping.
The PSNI said nothing was said to the girl - who ran off and called a friend - and no attempt was made to get her into the car. The driver of the car is described as being tanned with black cropped hair.
A spokesman said: "Police are aware of rumours circulating on social networking sites regarding these reports and we would like to reassure local people that they should not be unduly alarmed."