There were around 60 students, teachers and staff members in the single-storey building when the accident happened in Jhalawar district, some 322 kilometres, 200 miles, from the state capital Jaipur.
Kishore said the structure collapsed when students were attending their classes early on Friday.
Villagers rushed to the site and rescued many injured children who were taken to the closest medical facilities.
The building was in a dilapidated condition and several complaints had been previously been raised about it.
It had also been raining heavily in the area over the past few days.
Prime Minister Narendra Modi said he was deeply saddened by the tragic incident.
“My thoughts are with the affected students and their families in this difficult hour,” Modi said in a statement posted on his social media.
“Praying for the speedy recovery of the injured. Authorities are providing all possible assistance to those affected,” the premier added.
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