The protests began in the north-east as an outcry against economic hardship and rising prices, but turned political in many places, with slogans chanted against Supreme Leader Ayatollah Ali Khamenei, Mr Rouhani and Iran's interventionist foreign policy in the region. Calls by President Trump and Secretary of State Rex Tillerson for Iran to respect the rights of demonstrators were seized on by Iranian officials who sought to blame the protests on outsiders.
Iranian President Hassan Rouhani, whose administration struck the 2015 nuclear deal with world powers, campaigned on freeing the men, though they remain detained.
"I do not know whether yesterday's shooting was done by rally participants or the police and this issue is being investigated", Khademi was quoted by ILNA as saying.
Hundreds of people have been arrested.
So far, security forces appear to have shown some restraint, in an apparent attempt to avoid escalating tensions. Correspondents say it would be a significant escalation were they to become officially involved in policing the protests.
"The government will show no tolerance for those who damage public properties, violate public order and create unrest in the society", he said in remarks on state TV.
Mr Rouhani described the United States president as an "enemy of the Iranian nation from the top of his head to his very toes" after Mr Trump said Iranians were "finally getting wise as to how their money and wealth is being stolen and squandered on terrorism".
While police have arrested some protesters, the country's powerful Revolutionary Guard and its affiliates have not intervened as they have in other unauthorised demonstrations since the 2009 election.