Villagers in Khairabad in Uttar Pradesh took the law into their own hands after being gripped by panic over daily attacks that according to media reports have now left 14 children dead since January.
The three children, all aged under 12, were killed by packs of dogs in separate incidents on Tuesday as they collected mangoes in fields outside the village.
A 2001 animal welfare law outlawed the killing of stray dogs. But the Khairabad villagers shot dead three and beat to death at least 10 others.
"Our investigations revealed the children were alone at the time of attacks," district police chief Sureshrao A. Kulkarni told AFP, confirming the three latest deaths.
He said there had been several previous deaths since January but did not give a figure.
Authorities linked the surge in attacks to the closure of a slaughterhouse in the area in November, where most of the dogs previously fed on animal carcasses.
India has an estimated 30 million stray dogs, with roughly 17 million dog bites reported each year. Nearly 20,000 people die of rabies in the country each year, according to World Health Organization figures from 2014.
Incidents of angry residents attacking strays are growing across India.
Last month two men were arrested in New Delhi after they beat a stray to death because they were annoyed by its barking. A video of the incident was widely shared on social media.
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