A one-year-old infant was shot dead by a three-year-old boy who had picked up an unattended gun in a Cleveland home, sparking a police chief to plea for the US to end its "fascination" with firearms.

Police chief Calvin Williams told media outside the address where the fatal shooting took place that it was a "sad day for Cleveland".

"A one-year-old child lost his life," he said. "This fascination that we have with handguns, not just in this city but in this country, has to stop. This is a senseless loss of life."

Circumstances for the incident, including where the three-year-old found the gun and why it was not secured, were not immediately clear. Police have opened an investigation.

"A three-year-old can't be held accountable for a tragedy like this. There have to be adults that either supplied the weapons, had charge of the weapons or knew the weapons were there and didn't do anything to safeguard them," Williams said.

Authorities said at least one person was at the address at the time of the shooting. The victim, named as Braylon Robinson, suffered gun wounds to the head and was pronounced dead at a local hospital.