- Carlos Moore is asking for a "full and transparent" probe into what happened.
- The child, Aderrien Murry, was shot in the chest inside his home after he called 911 for a domestic disturbance, his mother said.
A lawyer for an 11-year-old boy shot by police in Mississippi says there is "no way" officers could have mistaken the child for an adult.
Carlos Moore is asking for a "full and transparent" probe into what happened.
The child, Aderrien Murry, was shot in the chest inside his home after he called 911 for a domestic disturbance, his mother said.
The officer who shot him has been placed on leave pending an investigation.
The boy survived the shooting and is recovering at home after being released from a local hospital, where he was treated for a collapsed lung, fractured ribs and a lacerated liver, according to the family.
They say he was shot after an officer responding to the call asked for everyone inside the home to come out with their hands up and the boy walked around a hallway corner into the living area.
Both his mother and the officer helped render aid until medics arrived, the family has said.
Mr Moore said that Aderrien Murry stands about 4ft 10in (1.47m), and could not have been mistaken for the adult man who was the subject of the domestic disturbance call.
"You couldn't perceive that he was an adult or a threat, because he didn't have anything in his hands," Mr Moore told the BBC on Friday. "I don't see why he shot him."
Mr Moore added that the boy was just obeying his mother, who had asked him to call the police for assistance after she grew concerned by the behaviour of the father of another of her children.
He said the family is relieved the boy survived but are shaken by the incident, including Aderrien.
"He doesn't understand and wants to know what did he do wrong and why did the cop shoot him, and no one can answer that question," Mr Moore said.
The officer has been placed on leave with pay, according to the lawyer.
The Indianola Police Department has yet to comment to media on the incident.
The child's mother, Nakala Murry, and Mr Moore held a sit-in with supporters outside the Indianola city hall on Thursday. They are calling for body-camera footage of the incident to be released and for the police officer involved to be fired.
Mr Moore said he plans to file a federal civil rights lawsuit against the city, the officer and the chief of police on Tuesday.
The Mississippi Bureau of Investigation has said it is "currently assessing this critical incident and gathering evidence", and will submit its findings to the state attorney general's office.