A safety alert was issued to Hartlepool primary schools after a man tried to speak to a pupil.
The man, believed to be aged about 40, is said to have approached the perimeter fence of Ward Jackson C of E Primary School, in Clark Street, on Thursday lunchtime.
He is reported to have tried to engage a child in conversation but left, possibly in a red car, before staff could find out what he was doing.
Police and the school stressed that no children were in danger at any time.
A spokesman for Ward Jackson Primary School said: “A man tried to engage in conversation with a pupil who was securely inside the school perimeter fence.
“The safety of our pupils and community is paramount and we immediately notified the police and have notified our parents and urged them to be vigilant.”
A spokesman for Hartlepool Borough Council added: “The safety of children in Hartlepool is our top priority, and as soon as the school made us aware, we notified our other schools as a precaution.”
The man concerned was described as having black hair and brown skin, and was approximately 5ft 8in-tall.
Someone in a red Volvo is said to have been seen acting suspiciously at around the same time but when a member of staff approached they drove off.
Cleveland Police added said: “He left the area, possibly in a red car which had also been seen nearby, before staff could ascertain what he was doing there.
“At no time was any child in danger and inquiries into this report are on-going.”
Other primary schools across Hartlepool posted alerts on their Facebook pages.
Greatham Primary School also sent text messages to parents about the incident.
One primary school said on Facebook following the incident: “We ask you all to be vigilant at all times and if anyone notices anything suspicious please report this to school.
“Be assured all staff within school will also be vigilant.”
Last week, Manor Community Academy put a message on its Facebook page telling people to be on their guard after reports of someone offering a lift to children.
The school urged people to be vigilant after they were made aware of a fair-haired male, driving a white van.