The train collided with the bus carrying some 38 children to school in the southern state of Telangana, dragging the mangled vehicle several hundred metres down the tracks, local media reports said.
A senior police officer said "11 students and the bus driver were killed", while a railway official told AFP that he feared as many as 25 children were dead.
The train hit the bus at an unmanned railway crossing in the village of Masaipet some 62 kilometres (38 miles) from the state capital Hyderabad, said K. Samba Siva Rao, a spokesman for South Central Railway.
Crowds poured over the accident site in Medak district trying to move twisted metal to retrieve small bodies trapped in the wreckage, local television footage showed.
Parents who reached the site were seen wailing, crouching next to their dead children as a small crane and a digger tried to lift wreckage from the tracks.
Anger among those in the crowd was growing, with some calling for the sacking of senior railway officials over the tragedy, local station TV9 showed.
The students went to Kakatiya Techno School, in the nearby town of Toopran, an official told AFP. The school teaches children as young as two and a half years old, according to its website.
The train was travelling from the city of Nanded in Maharashtra state to Hyderabad in newly-formed neighbouring Telangana, which was this year carved out of Andhra Pradesh state.
No one on the train was badly injured, officials said.
"So far 11 children and one school bus driver died. Sixteen children are injured and have been shifted to hospitals," local police deputy inspector general N Suryanaarayana said.
"The cause of the accident and whose mistake it is we are investigating," he told AFP.
Rao told AFP that some 38 children were on board the bus and "as per present information about 25 school children seem to have been killed."
- Suspicion falls on bus driver -
An Indian Railways spokesman said it appeared that the bus driver had not stopped before crossing the tracks, adding that 20 ambulances were on site.
"Prima facie it seems proper precaution wasn't taken by the bus driver (before crossing the tracks)" spokesman Anil Saxena told reporters. "This is a very unfortunate incident," he added.
Deadly train accidents are common on India's railways, whose vast and rundown network carries tens of millions of people daily.
In 2012 a government report said almost 15,000 people were killed every year on the network, describing the deaths as an annual "massacre" due mainly to poor safety standards.
In May, 26 people were killed when a passenger express travelling in the northern state of Uttar Pradesh ploughed into a stationary freight train.
An express train ploughed into a crowd of Hindu pilgrims in eastern India in August last year, killing 37 and triggering a riot that left one of the drivers dead and carriages ablaze.