The state-owned Iran daily says the relatives, who came to watch the hanging of two convicts, started a scuffle, prompting the police to open fire.
The paper's report on Thursday says 27 other people were injured in the melee.
It says the incident took place on Tuesday afternoon in the town of Sirjan, some 620 miles south of Tehran, where the two convicts were hanged for armed robbery.
The men were initially to be hanged on Tuesday morning, but a similar scuffle disrupted that execution.
Murder, rape, armed robbery, kidnapping and drug trafficking are crimes punishable with the death penalty in Iran.