Additional Superintendent of Police Manoj Kumar Rai said that after the driver lost control over the bus, it broke through the road divider in the city's Kanadia area and collided with a truck coming from the opposite direction.
The children were on their way home from school, he said.
"Earlier we had the information that six persons were killed. Later, it was clarified that four school children and the bus driver died in the accident. Another student is in a critical condition and on life support. The bus driver's assistant is also in a critical condition," Rai said.
The bus driver was identified as Rahul Sisodiya (35).
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Front portion of the bus was badly damaged in the collision, the police official said.
"We have seized the truck and are searching for its driver who fled from the spot," the ASP said.
District collector Nishant Warwade said a magisterial inquiry has been ordered into the incident.
Madhya Pradesh Home Minister Bhupendra Singh said he has asked for a report from the Deputy Inspector General of Police as well as transport authorities.
"The government had issued guidelines for schools after a school bus accident in Bhopal. We will fix the responsibility of schools to ensure the safety of children," he said.