Police have increased their patrols around Bromley, southeast London, after receiving four separate reports of "perceived" attempted abductions of children.
On 30 April, an 11-year-old boy was approached by a man in a black van on Whitmore Road in Beckenham who asked him if he wanted a lift.
On the same day, an eight-year-old boy was reportedly approached by a man in the wooded area of Kelsey Park.
A third boy said he was followed in the street by a man on Wednesday and reported the incident to staff at his school the following day.
A "lack of similarities" with the incident indicated it was not linked with the first two reports, the Metropolitan Police said.
On Friday, police were alerted to an incident in The Glades shopping centre where two males were reported to have been walking behind a girl, and tried to grab her hand before walking off.
The Met said the incident is not believed to be linked to any of the others.
Superintendent Andy Brittain said: "I am aware of varying reports online both in the news and on social media and I fully understand the concerns of parents in light of these reports.
"I would encourage the public to remain vigilant, but not to be unduly alarmed.
"Child kidnappings or abductions are, thankfully, incredibly rare, but we are not complacent.
"In order to provide reassurance to the community we have heightened our visible presence in areas where youngsters may gather and I urge anyone who feels worried or concerned to approach my officers.
"I would strongly encourage members of the public to approach our officers if they have any concerns or have any information that could prove to be beneficial to our investigations."
None of the children were abducted or harmed in any of the four reported incidents, the Met said.
Anyone with information should contact police on 101 or tweet @MetCC. In an emergency always dial 999.