Sunday night was the deadliest since the angry demonstrations broke out on Thursday and spread across the country in the biggest test for the regime since mass protests in 2009.
Six people were killed in the western town of Tuyserkan after shots were fired, state television reported, while a local lawmaker said two people had been shot dead in the southwestern town of Izeh.
Two others, included a teenage boy, were run down and killed by a fire engine stolen by protesters in the western town of Dorud, the state broadcaster said, bringing the total death toll in the protests to 12.
"Criticism and protest are an opportunity not a threat," Rouhani said in a statement on the presidency website, adding that the Iranian people would "respond to the rioters and lawbreakers".
"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."
Pro-regime rallies were held across several towns and cities. Videos on social media showed anti-government protests in cities including Kermanshah, Khorramabad and Shahinshahr.
A school for clergy and government buildings were torched in the northwestern town of Takestan and videos showed police using tear gas and water cannon to disperse a small protest in Tehran's Enghelab Square on Sunday evening.
The authorities did not give details on who was responsible for the fatal shootings.
'Country must have discipline'
The authorities have confirmed more than 400 people were arrested since the outbreak of the unrest, of which around 100 have been freed.
Judiciary chief Ayatollah Sadegh Larijani joined Rouhani in warning against illegal action.
"Those who have rightful demands must be guided in lawful ways and those who riot and commit sabotage and chaos and set fire to public property... must be confronted decisively," he told the state broadcaster.
"The country must have discipline," Larijani added.
Verifying rumours and videos remained challenging due to travel restrictions and sporadic blocks on mobile internet and popular social media sites including Telegram and Instagram.
US President Donald Trump, a fierce critic of Tehran, used one of his first tweets of 2018 to again lash out at a favourite target.
"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!"
