An eight-year-old boy was shot and killed in police crossfire in northern India, an officer said on Thursday.

Madhav Bharadwaj was playing with friends in Uttar Pradesh state when he was shot dead in front of his grandfather late on Wednesday.

Police said they went into the boy's village on a tip-off that suspected robbers were hiding out there, and it was unclear who fired the bullet that struck him.

Villagers, however, told local media that only police were shooting.

“Three policemen came to the village and asked the (suspects) to gather at the terrace of a nearby temple for a talk. But suddenly the cops began firing,” the boy's grandfather told the Times of India.

“My poor grandson was playing nearby and got hit. I froze for a moment. I was unable to understand what had happened.” Rajesh Kumar Sonker, a superintendent of police in Mathura district where the incident took place, told AFP an investigation was under way.

“We are probing the case and will soon get to know how the child got hit and killed,” he said.

Uttar Pradesh Chief Minister Yogi Adityanath offered his condolences to the family and compensation of 500,000 rupees ($7,835).

The state has one of the highest crime rates in India, an issue that Adityanath pledged to tackle with tough policing when he was named chief minister last March.

Rights groups have however accused him of abusing his power after he reportedly said at a rally that criminals would “either be sent to jail or killed in police encounters”.

Police in Uttar Pradesh and other Indian states have been accused of faking “encounters” with suspects to carry out extrajudicial killings.

“It has observed that even if the law and order situation is grave, the state cannot resort to such mechanism, which may result in the extrajudicial killings of the alleged criminals,” India's National Human Rights Commission said in a statement responding to Adityanath's comments.

Uttar Pradesh police have killed 33 people since Adityanath came to power according to figures in the Indian Express newspaper.