Six protesters were killed in clashes with security forces as they tried to storm a police station in the town of Qahderijan, which has a population of around 30,000, the broadcaster said.
A member of the Revolutionary Guards was killed in nearby Kahriz Sang, and a passerby in the town of Kahriz Sang.
Around 100 people were arrested overnight in the same region, Iranian state television reported.
Earlier reports had already said a police officer was killed and three others injured in Najafabad after being shot with a hunting rifle.
About 450 people have been arrested in Tehran, officials said on Tuesday.
The capital has been less affected by the protests than smaller towns and cities.
Austerity sparked protests
Protests began last Thursday in second city Mashhad and quickly spread across the country.
Analysts blame the unrest on austerity measures introduced by President Hassan Rouhani since he came to power in 2013, including another round of welfare cuts and fuel price rises in the latest budget announced a few weeks ago.
At a cabinet meeting Sunday, Rouhani said government bodies must provide "space for criticism" but also warned protesters that violence was unacceptable.
Rouhani came to power in 2013 promising to mend the economy and ease social tensions but the high cost of living and 12 percent unemployment have left many feeling that progress is too slow.
The young are most affected, with as many as 40 percent out of work according to analysts, and rural areas particularly hard-hit.
"Even if quite a few people don't agree with the violence they've seen, they certainly understand where this is coming from," says Eric Randolphe, AFP's correspondent in Tehran.
Tension "has been bubbling away for a long time", he told RFI.
"Everybody understands the frustrations, especially of the young people.There is the feeling that the government has just not been responding adequately to issues such as high prices."
While denouncing the protests, the regime knows it has to improve living standards, Randolphe said.
"One official said on Monday that this was a proxy war against Iran. But everybody agrees, even on the conservative side, that something needs to be done about the economy."
Turkey warns against "external interventions"
Turkey on Tuesday said that "common sense should prevail to prevent any escalation."
"Turkey is concerned by news the protests in Iran ... are spreading, causing casualties and also the fact that some public buildings were damaged," the foreign ministry said in a statement.
"We believe that violence and provocations should be avoided," it said, warning against "external interventions."