The deaths have triggered a war of words between the government of Chief Minister Nitish Kumar, which blamed the supplier of foods for the tragedy, and an aggressive opposition including the estranged ally BJP.
The unprecedented deaths, in Dandaman village in Saran, about 100 km from Patna, have also sparked off street protests in Bihar.
At least 10 school students were battling for life in a Patna hospital after consuming the free food at their school as part of the mid day meal scheme Tuesday.
The national mid day meal scheme is the world's largest school feeding programme reaching out to some 12 crore children in 12.65 lakh schools and education centres across India.
Hundreds have been protesting in Saran since Tuesday night demanding action against government officials who oversaw the mid-day meal scheme.
A case has been registered against the school's headmistress, Meena Devi, and other teachers. All of them are absconding.
Amarjeet Singh, principal secretary in the education ministry, said he suspected the deaths occurred due to organo phosphorous poisoning caused by traces of insecticides.
Over two dozen sick children have been brought to the Patna Medical College and Hospital after their condition deteriorated. "Ten children are still critical," a hospital official said.
Kanti Kumari, a student of Class IV, said at a Patna hospital: "The meal we got did not taste the same. That's why many students didn't eat. But we ate it after the teacher scolded us.
"When I complained of stomach ache, the lady teacher told us to go home. As I stepped out of the school, I fainted."
Police said the children had been served rice with potato and soyabean.
Central Minister of Human Resource Development M.M. Pallam Raju said in New Delhi: "It is very sad to know about ... food poisoning. We have taken serious note of what has happened."
He put the number of dead children at 20 and said the man who cooked the meal also died. Another 21 children were in hospital. Bihar officials said the death toll was 23 including the cook.
Raju said: "It looks like contaminated food... but we are awaiting the forensic report."
Saran District Magistrate Abhijit Sinha said earlier that 10 children died after eating the meal at the Dharamsati Primary School in Masrakh.
Women who lost their children wailed in Dandaman village.
"We did not realize that our children would not return home alive," lamented a woman whose two sons, Prahlad and Rahul, died in the tragedy.
A pall of gloom hung over Dandaman village where the students and the cook died.
According to statistics, 22,102 government schools in Bihar that serve mid-day meals do not have kitchens. In 7,235 schools, the storage room is under construction.
The Bharatiya Janata Party (BJP) called Nitish Kumar insensitive.
"The chief minister, instead of showing promptness in evacuating the children to a better medical facility, has announced a ex-gratia amount of Rs.2 lakh for the children who died," BJP's Rajiv Pratap Rudy said.
In Bihar, the mid-day meal scheme has often into controversy. In the past, dead lizards, frogs, insects and even a rat have been found in food cooked for the mid-day meal in schools.
The National Commission for Protection of Child Rights (NCPCR) Wednesday called for closer monitoring of the mid-day meal scheme.
"It is deeply shocking that the mid-day meal scheme is taking children's life. The government needs to closely monitor the scheme through regular inspections," NCPCR chairperson Kushal Singh told IANS.