The toll from Friday's fire is expected to rise, police said.
"Seventy-seven bodies (of children) have been recovered," senior police official S Natarajani told AFP from the town of Kumbhakonam where the blaze started at around 11:00 (05:30 GMT).
"Thirty-four have been admitted to the local government hospital," he said.
"The death toll is likely to go up as some of those admitted are in a critical condition," he said.
The pupils of the Krishna Primary School were aged between six and 13, officials at the site of the fire said.
Weeping parents rushed to the school building to look for their children as bodies were being removed. Others crowded the government hospital about 350km from Chennai, the state capital.
A preliminary inquiry showed the "fire was caused by an open firewood stove in the kitchen of the school where the midday meal for the children was being cooked," Natarajani said.
It spread from the kitchen to the adjacent thatched portion of school and from there to a one-storey building where most of the 350 children were in class, Natarajani said.