Ravindra Kumar, the additional director general of police in the city of Patna, told reporters that forensic tests revealed that the samples contained the pesticide monocrotophos in levels that were "very toxic" for humans.
The free midday meal was served to the children Tuesday in Gandamal village in Masrakh block, 80 kilometers (50 miles) north of Patna, the Bihar state capital.
Twenty-three children between the ages of 5 and 12 died from eating the meal and many others fell ill.
No arrests have been made in the case.
Authorities discovered a container of insecticide in the school's cooking area next to the vegetable oil and mustard oil, but it wasn't yet known if that container was the source, officials have said.
India's midday meal plan is one of the world's biggest school nutrition programs. State governments can decide on menus and timings of the meals, depending on local conditions and availability of food rations.
It is seen as an incentive for poor parents to send their children to school and currently covers some 120 million children across the country.
It's also part of an effort to address concerns about malnutrition, which the government says nearly half of all Indian children suffer from.
While complaints about the quality of the food served and the lack of hygiene in the program are routine, the incident in Bihar appeared to be unprecedented for the massive food program.