US police shot and wounded a 13-year-old boy carrying a replica handgun on the anniversary of mass protests sparked by a black man's death in police custody, police said.

Baltimore Police Commissioner Kevin Davis told reporters near the scene of Wednesday's shooting that two officers spotted the teenager carrying what appeared to be a firearm, identified themselves and gave chase when he ran away.

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Wednesday marked the one-year anniversary of protests and clashes with police in Baltimore following the death of an unarmed black man, Freddie Gray, in police custody.

"This is exactly what our community expects a police officer to do when they see someone with a firearm," Davis said. "Why this young man chose to flee on foot when he was approached by two Baltimore police officers, I don't know."

Police subsequently took the boy's mother in for questioning, although she was not arrested. 

Davis said the teen's injuries were not life threatening.

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Some 2,000 National Guards flooded Baltimore a year ago, clashing with angry protesters. 

Gray's death was one of several high-profile cases in the US of a black man dying at the hands of police - a situation that has stirred resentment among black Americans who believe they are targeted by police.

That anger also sparked coast-to-coast demonstrations in major US cities after a white policeman shot dead an unarmed black teenager in the St Louis suburb of Ferguson in August 2014. 

Source: Agencies