"The bus went out of control of the driver and plunged into a ditch after breaking into the roadside fence near Lillah Interchange," a police official said.
He identified Mujahid Hussain, student of class 4, Waqas of class 8, Irfan Gondal of class 8 and Ahmad Bhatti of class 6 as dead.
"Rest of the children could not be identified so far," the official added. Another official, Mohammed Sabir, said that the bus swerved off the road into a ditch, then smashed into a roadside safety barrier.
Many of the children were under 10. Beside the dead, at least 15 were seriously injured.
A school official said that the Principal of the school, Mukhtar Ahmad was accompanying children "but in his own car". The official said that the Principal had informed police about the accident.
Police rushed to the spot and initiated rescue work. "Some children died on the spot while others were proclaimed dead in hospitals," he added.
The injured were shifted to Fauji Foundation Hospitals in Chakwal and Kalar Kahar.
Some injured were taken to Civil Hospital, Chakwal, where some of them were in unconscious condition, a doctor engaged in emergency treatment said.
The report of the accident created panic among parents of the children who rushed to the spot while large number of parents and relatives reached the school to inquire about the fate of their children. Doctors expressed fear that the number of dead may increase.
AGENCIES ADD: President General Pervez Musharraf on Sunday expressed a deep sense of shock and sorrow over the tragic death of school children in the road accident on the motorway.
The President said he was deeply grieved to learn about the loss of innocent lives in the mishap. He directed the concerned authorities to look into the cause behind the incident to prevent occurrence of such accidents in the future.
Information Minister Sheikh Rashid Ahmed said Prime Minister Shaukat Aziz has ordered probe into the bus accident.
Talking to the children of Rawalpindi Radiant School, who received injuries in a road accident, he said the government would take effective steps in order to avoid such incidents.
He said Prime Minister has also announced Rs100,000 each for deceased and Rs25,000 each for injured. The government will bear all expenditures of treatment," he added.
Punjab Chief Minister Chaudhry Pervaiz Elahi has expressed deep sense of sorrow and grief over the death of school children.
In a condolence message, the chief minister expressed his sympathies with the bereaved families and said that he equally shared their grief.
He announced financial assistance of Rs100,000 to the heirs of each child who lost his life, while Rs50,000 would be paid to each injured.