That brings the estimated death toll to 21 in unrest linked to the protests that began last Thursday in the second city of Mashhad and quickly spread across the country.
Khademi said the cause of deaths in Izeh wasn't immediately known.
"A rioter took advantage of the situation in the city of Najafabad and fired shots at police forces with a hunting rifle", Saeed Montazer al-Mahdi, a police spokesman, told the Iranian state broadcaster as cited by the news agency.
Hundreds of people have been arrested following the clashes. Two other people people died when protesters are said to have seized a fire engine and ran into a vehicle.
The protests were fanned in part by messages sent on the Telegram messaging app, which authorities blocked on Sunday along with Instagram.
Iranian judiciary chief Ayatollah Sadegh Larijani urged authorities to strongly confront rioters, state TV reported.
US President Donald Trump has used the protests to repeatedly bash the Iranian government and warned it against any human rights abuses, building on his crusade against the 2015 nuclear deal that Iran signed with world powers under Trump's predecessor, Barack Obama.
"The problems of the people are not simply economic in nature".
"Iran is failing at every level despite the bad deal made with them by the Obama Administration", he wrote, adding that the Iranian people were "hungry for food & for freedom".
Arctic air arrives just in time to ring in New Year
Places such as Boston are on track to break the longest stretch of below-20-degrees days in its recorded history. The combination of cold air and wind will drive wind chill readings down to below zero into Monday morning.
A recent increase in egg and poultry prices by as much as 40%, which the government has blamed on a cull over avian flu fears, appears to have been the spark for the economic protests.
Meanwhile, Iranian President Hassan Rouhani said that the ongoing wave of protests may have been partially stirred up by external forces interested in destabilizing the Islamic Republic.
Israeli Prime Minister Benjamin Netanyahu, calling the protesters "brave" and "heroic", said in a video posted to YouTube on Monday that the protesters sought freedom, justice and 'the basic liberties that have been denied to them for decades'.
Despite an appeal by Rowhani on Sunday for the protesters to act peacefully - and during which he supported their right to express their opinions - witnesses reported violence across the country.
"The great Iranian people have been repressed for many years", he wrote.
"It's clear there's a kind of discontent that's sweeping Iran over broad issues".
The European Union on Monday pushed Iran to guarantee the right to protest and separately British Foreign Secretary Boris Johnson said "the United Kingdom is watching events in Iran closely".
Iran's economy has improved since the nuclear deal, which saw Iran agree to limit its enrichment of uranium in exchange for the end of some worldwide sanctions. Unemployment remains high, and official inflation has crept up to 10% again.
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