District Magistrate Shambhu Nath had earlier put the toll at 15, but officials later confirmed 13 deaths.
The bus was carrying students to J S Vidyaniketan school which had opened flouting the district magistrate's orders to keep all schools up to class VIII closed till tomorrow in view of intense cold, officials said.
The mishap occurred near Asadnagar village under Aliganj Kotwali police station area in Etah, which is four hours drive from the national capital.
This is the second incident in six months in the state involving school kids after a school mini-bus was hit by a train at an unmanned railway crossing in Bhadohi district which left 8 children dead and 14 others injured.
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Nath said soon after getting the news, senior officials rushed to the accident spot and supervised rescue and relief operations.
A crane had to be deployed to retrieve the bus which lay mangled as a large crowd of onlookers gathered at the scene. Gas cutters were used to open up the body of the bus for rescuing the trapped children.
Nath said orders have been issued to cancel the recognition of the school whose manager and principal defied the district administration's directives and opened the school.
FIR is being lodged against the school management.
Eyewitnesses said the truck, coming from the opposite direction at a high speed, hit the bus which overturned under the impact of the collision.
The front portion of the bus was ripped open under the impact of the collision.
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