Reports vary as to the number of those who have died but officials on Wednesday put the toll at 22, with another 25 in hospital, as well as the school cook. Three of the children were in serious condition, Associated Press reported.
The children, between the ages of five and 12, fell ill after eating the lunch, of rice and lentils, at the village of Chapra, in the poverty-stricken state of Bihar, on Tuesday. The meal is believed to have been contaminated with pesticides.
"We are trying hard to save the children admitted [here] but the condition of some of them remains critical," said Dr Amarkant Jha Amar, superintendent of the Patna Medical College and Hospital.
Angry parents disinterred the hastily buried bodies of some of the victims and displayed them outside the school in protest. Demonstrators pelted a police station with stones, set ablaze buses and chanted slogans denouncing the state government.
India's free school meals programme is one of the biggest such schemes anywhere in the world, covering more than 100 million children. Prices of meat, fruit or fresh vegetables have soared in recent years, leaving parents in poorer families reliant on school lunches to ensure adequate levels of nutrition. But the scheme is plagued by waste and corruption, and incidents of poisoning are common - though they are rarely this serious.
Early tests showed that the food at the school may have been contaminated with pesticides used on rice and wheat crops in the area. Staff stopped serving the meal after children began vomiting.
A senior government health official in Delhi said one possibility was that ingredients had been stored too close to dangerous chemicals. "Washing before cooking would have made no difference," he told the Guardian.
Parents in Chapra first took their children to the rudimentary local health centre before they were transferred to local hospitals. Even in major metropolises India has no functioning ambulance service; in rural areas cars, rickshaws or even carts are used to carry the ill or injured.
"As soon as my son returned from school, we rushed to the hospital with him. His condition was not good. He was vomiting and said his stomach was hurting," one parent told the Indian broadcaster CBN-IBN.
Ram Bachan Rai, a villager, accused local officials of delays, which he said had caused the deaths of many children.
"It was sheer callousness on the part of the officials. They wasted much time before shifting the kids to the hospitals, and necessary medicines were not available ," Rai, 37, told the Guardian.
According to Abhijeet Sinha, a senior government official in Chapra, two children had died even before they reached the local clinic, with seven more dead before they could be brought to the nearest hospital.
"The doctors did their best to save the children but there was so much poison in their food that the doctors couldn't save them all," Sinha told NDTV news channel.
Ajay Prasad, a farmer in Chapra, said he had brought up his only daughter, who died on Tuesday afternoon, "like a son". Male children are traditionally favoured in conservative Indian rural areas. "I never knew I would have to pay such a price for admitting my baby to a government school," he said.
The authorities had suspended a food inspector and registered a case of criminal negligence against the school headmistress, who fled after the incident and was now sought by police, said PK Shahi, Bihar's education minister.
"In spite of the cook's complaint [over the smell of the cooking oil used for the food], the headmistress insisted on its use and the cook made the food. The children had also complained about the food to the cook," he told a news conference.
School meals in India are provided by contractors, many of whom use substandard ingredients and pay local officials to turn a blind eye to the fact. Grain purchased by the government for distribution is often poorly stored.
Dunu Roy, director of the Hazards Centre thinktank, in Delhi, and a chemical engineer, said heavy contamination of ingredients would have been noticeable.
"Those kind of levels, particularly after the food was cooked, should have been spotted by someone. Some kind of collusion, all the way up the chain, would have been necessary," he said.
But the cause of the tragedy may have been negligence and ignorance rather than corruption: there were reports on Wednesday that potatoes and a sack of pesticides had been found side by side at the school headmaster's home.
The Bihar state chief minister, Nitish Kumar, has ordered an inquiry and announced that compensation of 200,000 rupees (£2,300) will be paid to the dead children's parents.
According to the World Bank, 43% of Indian children are underweight. That is the highest level in the world and a figure that has remained constant for at least 20 years. In China the figure is only 7%; in sub-Saharan Africa it averages 28%. Poor nutrition among lactating and pregnant mothers means the effects of postnatal malnutrition for children are exacerbated.
The Indian prime minister, Manmohan Singh, has described infant malnutrition levels in India as a "national shame".
The government, led by the Congress party, is pushing for a $21bn (£14bn) expansion of the country's food subsidy programme.
Roy, of the Hazards Centre, said effective, safe distribution to the hundreds of millions suffering from poor diet or malnutrition depended on sufficient political will.
"If you want to invest, you can have a very efficient system," he said. "But they don't want to invest. This is an election year. The politicians are not interested in getting food to people: they are interested in votes."
Additional reporting by Manoj Chaurasia, Patna