The accident occurred at the Central Railway's Gulabganj railway station, about 20 km from here, after a wrong announcement was allegedly made about the train.
The railway station has no foot over bridge, because of which people mostly cross the tracks to reach the station.
This morning, at the station an announcement was made for a train leaving on the up line. Hearing the announcement, some people, including the children, tried to cross the down line by crawling under a goods train which was stationed there.
The children - Mohammad Ali (5) and his eight-year-old sister, whose name was yet to be ascertained - died on the spot, they said.
Later, angry villagers disrupted rail traffic on the route by blocking both the up and down tracks and also damaged some railway property, they said.
Because of this several trains scheduled on the route were stopped at Bina, Bhopal and Vidisha railway stations, they added.