That brings the number of people killed in six days of unrest to at least 21 people.
State TV says six rioters were killed in the town of Qahdarijan, during an attack on a police station. The clashes were sparked off as protesters tried to steal guns, according to reports.
Two people, a 20-year-old man and a boy aged 11, died in the town of Khomeinishahr and a member of the Revolutionary Guards was killed in nearby Kahriz Sang.
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.
Another 450 have been held over the last three days in the capital Tehran, according to the semi-official INLA.
The head of Tehran’s Revolutionary Court reportedly warned protesters they could potentially face the death penalty.
On Monday, a police officer was reportedly shot dead and three others wounded in Najafabad although it wasn’t clear if the officer was the same as the Revolutionary Guard member reported dead in Kahriz Sang.
The demonstrations, the largest to strike Iran since its disputed 2009 presidential election, have been sparked by anger over the country’s flagging economy and a jump in food prices.
Unemployment and inflation are very high, and a lifting of sanctions in January 2016 has failed to deliver the economic boom many hoped for.
President Hassan Rouhani has called for calm, warning that the government would not tolerate violence.
He said on the presidency’s website: “This is nothing.
“Our nation will deal with this minority who chant slogans against the law and people’s wishes, and insult the sanctities and values of the revolution.”
US President Donald Trump has tweeted in support of the protesters, writing: “The great Iranian people have been repressed for many years. They are hungry for food & for freedom. Along with human rights, the wealth of Iran is being looted. TIME FOR CHANGE!”
Turkey, meanwhile, said it was “concerned” protests were “spreading” and called for “common sense” to prevent “any escalation”.
The secretary of Iran’s Supreme National Security Council, Ali Shamkhani, blamed the UK, the US and Saudi Arabia for fomenting the protests on social media.
The protests began Thursday in the northeastern city of Mashhad, Iran’s second-largest, and quickly spread across the nation, with some protesters chanting against the government and the supreme leader, Ayatollah Ali Khamenei.
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Authorities have also blocked access to Instagram and the messaging app Telegram to try to damp down the protests. Both apps were used by activists to organise the demonstrations and share images and information.