Police in Arkansas are hunting for a man who opened fire in an an apparent road rage incident - killing a three-year-old boy who had been taken shopping by his grandmother.

Reports said that the boy’s grandmother was driving through the city of Little Rock on Saturday night when another motorist opened fire. Police said that at some point, the person started firing at her car because he thought she “wasn’t moving fast enough at a stop sign”.

The boy was struck at least once and was taken to a hospital where he died shortly afterwards. The grandmother was unhurt. None of the identities of those involved have yet been released.

Police Lt Steve McClanahan said investigators believed the boy and his grandmother “were completely innocent” and have no relationship with Saturday’s shooter, who was being sought.

He said the grandmother simply was “driving the car and was taking her grandson shopping when the incident occurred.”

Police hunt motorist who 'killed three-year-old in road rage incident'

Police said they were looking for an older black Chevrolet Impala. Police did not release a detailed description of the man who was driving it.

The Associated Press said that last month, a two-year-old girl was killed when a car drove by and someone fired into her vehicle; the shooter in that case has not been captured.

Police Chief Kenton Buckner said the road rage killings were frustrating for police departments and the community, especially because the young victims were “very innocent” and “can do very little to protect themselves.”