"We need to be careful of spreading untrue stories and unnecessarily alarming parents," Home Affairs and Law Minister K Shanmugam said in a Facebook post on Monday (Jan 22) morning.
He was commenting on some media reports describing last week's incidents at international schools in the Dover area as "kidnap scares".
In the case involving a United World College of South East Asia student on Jan 11, a man supposedly drove alongside her as she was waiting for the bus and told her to get in the van but she walked away and informed an adult.
Police later said that the man had "no ill intent" and offered the teen a ride because it was raining.
A second incident on Jan 16 involved a student from Tanglin Trust School. Reports said the student was walking to the school on Portsdown Road when a white van stopped near her and two occupants tried to entice her to get in.
Police clarified that the van was the school bus and that an attendant had noticed the girl wearing the school uniform and had offered to give her a lift to school. Authorities also said no one had alighted the bus to persuade the student.
"Some media reports have called them 'kidnap scares'," said Mr Shanmugam. "Media reports have said that the van occupants in one of the incidents had gotten out try to persuade one of the students to get into the van.
"That is untrue. The van provides transport services for the school, takes students to and from the school."
Mr Shanmugam said the authorities have investigated both incidents "thoroughly" and interviewed the people involved.
"There were no kidnap attempts," he wrote.
"It is important for young children to be taught to be careful when approached by strangers. At the same time, we need to be careful of spreading untrue stories and unnecessarily alarming parents."
"Certainly, we should teach our children not to get into any vehicles with strangers," he added.