It reported that clashes were sparked by rioters who tried to steal guns from the police station. It says all were shot by hunting rifles.
President Hassan Rouhani has played down the protests which began last Thursday, initially against price rises and corruption but which have taken on a wider anti-government sentiment.
According to Iran's security officials, scores of protesters were arrested.
Footage showed a ransacked private bank, broken windows, overturned cars and a firetruck that appeared to have been set ablaze.
Nine more people were killed overnight as protests against the government's economic policies, including looming price hikes, continued for a sixth day. Izeh is about 280 miles southwest of Iran's capital Tehran.
Hundreds of people have been arrested, including 450 people arrested in Tehran over three days, according to a report by the semi-official ILNA news agency.
One officer was killed and three were wounded in the protests in Iran, Reuters reports, citing state media.
The slaying marked the first security force member to be killed in the unrest. Two other people people died when protesters are said to have seized a fire engine and ran into a auto.
"I demand all prosecutors across the country to get involved and the approach should be strong", he said.
On Twitter, President Trump has sought to portray the unrest as the direct result of "Iranian citizens fed up with regime's corruption & its squandering of the nation's wealth to fund terrorism overseas".
About 100 people were detained overnight in the region where most of the unrest was occurring, near the central city of Isfahan, according to state TV. 'They are hungry for food & for freedom.
"We believe that there should be meaningful debate about the legitimate and important issues the protesters are raising and we look to the Iranian authorities to permit this", Johnson said in a statement.
The Iranian foreign ministry had also on Saturday strongly deplored the recent comments by Trump and State Department Spokeswoman Heather Nauert in support of the recent economic protests in Iran, describing them as "cheap, worthless and invalid".
Iran is still witnessing a wave of demonstrations, which are being held in many cities across the country.
Iranian authorities placed restrictions on some social media platforms used heavily in Iran, including Instagram and Telegram, in an attempt to prevent would-be protesters from using them to call for and organize further demonstrations.
He said that "we appeal to the Iranian government to respect the rights of demonstrators to assemble and raise their voice freely and peacefully". Iranians were hoping for improved living conditions following the nuclear deal and the lifting of some worldwide sanctions.
That improvement has not reached the average Iranian, however.
Tehran now sells its oil on the global market and has signed deals to purchase tens of billions of dollars' worth of Western aircraft. Unemployment remains high, and official inflation has crept up to 10% again.