“People of Izeh, like some other cities, held a protest against economic problems and unfortunately it led to the killing of two people and injuries to some others,” the area’s MP, Hedayatollah Khademi, told the ILNA news agency.
“I do not know yet whether last night’s shooting was by the protesters or by police,” he added.
Protests broke out in several towns and cities in a fourth night of demonstrations against economic problems.
Khademi said people in Izeh, a town of around 200,000 people, had broken the windows of banks as protests continued until around midnight (2030 GMT).
“That’s why police intervened to restore peace and order,” he told ILNA.
“The governor said it (the gunfire) was unlikely to be by police as they were not supposed to open fire,” he said in a separate interview with the reformist Etamad newspaper.
The deaths follow a report by the state broadcaster that two people died in the western town of Dorud overnight when they were hit by a fire engine stolen by protesters.
A total of six people have died since protests against economic hardship broke out across the country on Thursday.