Police have appealed for parents to remain calm after officers received five reports of children being approached by strangers in Stockport.
The incidents, which police are not linking, are alleged to have happened between 26 June and 1 July and involved children aged between 7 and 10.
Officers said they had received 22 further calls from worried parents since the first report.
One of the reports being investigated turned out to be false, police said.
Ch Insp Steve Dix said: "As a parent I fully understand the concern that residents are feeling following the reported incidents, however I now want to appeal for calm.
"Every call that has come into us has been thoroughly and robustly investigated and I want to reassure residents there is nothing whatsoever to link any of the incidents.
"We have spoken to schools and neighbourhood policing teams and have made appeals through the media.
"This has clearly heightened people's concerns but I would urge them to let their children out to play in exactly the same way they would have done a fortnight or so ago."
The first report involved a seven-year-old girl walking along Springwood Crescent, Romiley, on 26 June between 1300 and 1700 BST.
She said a man grabbed her from behind and asked her whether she wanted to see some puppies. The girl then ran off.
On 28 June, between 1700 and 1930 BST, near Brinnington medical centre, an eight-year-old boy said that he was grabbed by a man in a silver BMW, who asked him whether he wanted to buy a Nintendo DS.
The boy broke free and rode off.
Two days later a man is reported to have approached a 10-year-old girl on Wesley Street, Hazel Grove, and asked her whether she wanted to see some puppies, but the girl ran off.
On 1 July at about 2000 BST, a man is reported to have approached a seven-year-old boy on Coleridge Road and asked if he wanted some sweets.
The boy tried to run off and was grabbed by the man, but he struggled free and ran home.