After responding to the fight, the officers heard shots fired from the store.
Inside, they found that 27-year-old John Dalton Martinez had shot another man.
Martinez refused the officers' request to put down his semiautomatic handgun and pointed it at them.
Fearing for their lives and those of others inside the store, the officers fatally shot Martinez, said El Paso police spokesman Javier Sambrano.
The man Martinez injured, 27-year-old Julio Calderon, was treated at a local hospital for wounds to one hand and foot.
Police said Calderon got into a fight with a relative of Martinez and chased him into the store afterward.
The two officers were placed on routine administrative leave while officials investigate the shooting.
