The incident happened when the engine, on its way to Ara from Sasaram, hit the school van carrying 11 children when it was crossing the tracks at the unmanned crossing.
The vehicle was thrown off the tracks, police said.
The two children, who died on the way to hospital, have been identified as Vishal Kumar (10) and Amit Kumar (12), they said, adding the condition of others admitted to Ara Sadar hospital were critical.