The shooting in Ohio comes amid high racial tensions in the United States, with a grand jury set to announce whether a white policeman will be indicted for the fatal shooting in August of an unarmed black teenager in the St Louis suburb of Ferguson in Missouri.
Ohio was also the scene of another fatal shooting in August, when police responding to a 911 call shot and killed a black man, John Crawford, in a Walmart store while he was carrying a toy gun sold there.
In this latest incident, officers called to the scene on Saturday fired at the boy twice, hitting him at least once in the stomach, after reports that he was pointing a gun at people.
The boy, identified by the county medical examiner's office as Tamir Rice, died early Sunday, local newspaper The Plain Dealer reported.
One of the police officers was in his first year in the force, it said.
Audio released of a 911 call made to police records the caller saying the gun was "probably fake."
Both officers have been placed on administrative leave pending an investigation, as is standard in such cases, Cleveland police said in a statement.
"Upon arrival on scene, officers located the suspect and advised him to raise his hands," the statement said.
"The suspect did not comply with the officers' orders and reached to his waistband for the gun. Shots were fired and the suspect was struck in the torso."
The weapon which the 12-year-old suspect was in possession of is an 'airsoft' type replica gun resembling a semi-automatic pistol, with the orange safety indicator removed," it added.
Reports said surveillance footage from the playground was being used in the investigation.
In response to Saturday's shooting and the one that killed Crawford in August, state lawmaker Alicia Reese announced on Sunday that she would introduce a bill to require all toy guns to be brightly colored or have prominent fluorescent stripes.
"The shooting of John Crawford III devastated many people in our community and left us looking for answers," Reece said. "This bill is but one small step in addressing this tragedy and helping to prevent future deadly confrontations with someone who clearly presents little to no immediate threat or danger.”
"With Saturday's deadly shooting of a 12-year-old in Cleveland, it is becoming crystal clear that we need this law in Ohio," she added.
Brown's shooting in Ferguson over the summer led to weeks of violence in the St. Louis suburb of 21,000, which has an African-American majority and an overwhelmingly white police department and town government.
The death prompted a nationwide discussion about race and led to a Department of Justice probe into the Ferguson police department.
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