Schoolchildren are being warned to be vigilant after reports of three females being approached by men near All Saints Primary School.
Three people are believed to have been approached - with two of them being offered lifts - by strangers in the past week.
But police say they do not believe the incidents are linked.
In the latest incident, a young girl was grabbed from behind by a man who touched her thigh in Clayton-le-Moors on Monday afternoon.
It comes after a man in a car stopped on Charles Street to offer a girl a lift in the first incident on Wednesday, September 27.
In the afternoon of the same day, a young mother is also believed to have been approached by a stranger and offered a lift near Mercer Park.
Police are trying to trace a dog walker who may have witnessed the latest incident, which happened as a girl was walking along the canal towpath at around 4.30pm on Monday, October 2.
In a statement, Lancashire Police said: “She was grabbed from behind by a man who has touched her thigh and pulled at her bag.
“A male dog walker has walked on to the path from round a corner, disturbing the offender and the girl then ran off.”
Det Insp Mark Gillibrand, of Hyndburn Police, said: “We aren’t entirely sure what the offender’s motive was but that said, we are treating it very seriously.
“We appreciate that it will cause people some concern and so we have stepped up patrols in the area.
“We need to trace the dog walker described as white, between 30 and 40 years old, with a beard and a green jacket. He was walking a bulldog and may have some important information that could assist with our investigation. If you think this was you, please get in touch.
“We would also like to speak to anyone who may have seen a man acting suspiciously in the area around the time of the incident. Similarly, if you recognise the description of the offender, please make contact with us.”
He is described as white but very tanned, aged between 18 to 20, over 6ft tall with short cropped dark hair, full unkempt short facial hair and a pierced nose. He was wearing a red hooded top, white trainers, sunglasses and a gold ring on one of his hands.
Lancashire Police said they were also called to reports of ‘suspicious circumstances’ on Charles Street on Wednesday.
A spokesman said: “A girl was walking to school about 8.10am when a vehicle has pulled up alongside and a man has offered her a lift.
“She’s refused and the man’s driven off in the vehicle. She was not harmed. Enquiries are ongoing.”
All Saints headteacher Nicola Saporita-Clark said they have reported all the incidents to the police and parents were informed via a school app.
She said: “The police are dealing with the incidents. As a school we are just asking our parents to be extra vigilant when children are coming to school and are leaving at the end of the day.”
Clayton-le-Moors councillor Melissa Fisher, whose daughter has just left the school, told the Observer that parents had become ‘frightened’ over the safety of their children.
Coun Fisher said: “It’s really, really concerning. Three incidents in less than a week. It’s scary.
“We are calling for parents to be extremely vigilant.”
She added: “I know that a lot of parents in Clayton are very frightened now.
“We’ve shared warnings on social media telling people to be careful. When it’s so close to home it is very alarming.”
A newsletter sent home from the school to parents also asks families to “reiterate ‘stranger danger’ awareness to ensure their children have an ‘age appropriate’ understanding of risks and keeping themselves safe.”
The letter states: “It is very sad that we have to raise awareness within innocent children of such dangers but unfortunately something essential.”
Anyone with information can call police on 01254 353601 or if they fail to get an answer, 101, quoting incident reference 1003 of October 2.