Mesa police say 27-year-old Cesar Hernandez Enriquez died late Tuesday night after a confrontation with officers.
They say he fled from officers, then refused to put his gun down and ran toward police.
Police say one officer fired at Enriquez, but the gunshot wound he suffered to his upper body may have been self-inflicted.
Confirmation on the cause of Enriquez's death is pending the results of the forensic medical examination and subsequent criminal investigation.
Police say Enriquez was suspected in the fatal stabbing of 28-year-old Lindsay Esparaza on Tuesday morning.
She was found stabbed multiple times inside a Queen Creek home. Police say the motive remains unclear.
Copyright 2015 The Associated Press modified.