About 30 children remain in hospital in Patna, the Bihar state capital. Ten of the youngsters are in a critical condition.
It was earlier announced that eight children had died and 80 others were hospitalised.
They fell ill after eating a lunch of rice and lentils in Masrakh village in the Saran district on Tuesday.
They were rushed to hospital in the capital, some 50 miles (80km) south of the village, reports Sky News.
Some of the other sick children were taken to hospital in nearby Chaapra.
Sky Producer Neville Lazarus, in New Delhi, said: "Masrakh is in one of the poorest of the poor states in the country and in a remote place, so there weren't proper medical facilities."
The meal was cooked in the school kitchen, and police have seized all the ingredients used.
Bihar's Education Minister P K Shahi said a preliminary investigation suggested the food had traces of phosphorous, which is used to preserve rice and wheat.
"It is sad but true that 20 children died after eating their midday meal, which appears to be poisonous," the minister said.
Authorities have suspended a food inspector and registered a case of criminal negligence against the head teacher.
The father of an ill child, Raja Yadav, told reporters that his son was vomiting after returning from school.
"As soon as my boy returned from school, we rushed to the hospital with him. His condition was not good," he said.
Bihar state Chief Minister Nitish Kumar, who has also ordered an inquiry, announced that families of the dead children will be offered financial compensation of 200,000 rupees (£2,200).
The 20 children who died were buried near the school on Wednesday morning as angry residents armed with poles and sticks took to the streets in the city of Chhapra to protest against the state government over the children's deaths.
"Hundreds of angry people staged a protest in Saran since late Tuesday night, demanding stern action against government officials responsible for this shocking incident," district government official S K Mall said.
Free meals are offered to impoverished students in state-run schools as part of government welfare measures in many of India's 29 states
The lunches are hugely popular with poor families and educators see the meals as a way of increasing school attendance.
But children often suffer from food poisoning due to poor hygiene in school kitchens and the sometimes poor quality food.
More than 130 students were taken to hospital in the western city of Pune last year after eating lunch at school, the Times of India reported.
A probe revealed that the food served to them was contaminated with E coli bacteria, strains of which can cause food poisoning.
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