Ahmad Reza Radan, Iran's deputy police chief, also said that 300 protesters had been arrested following the violence.
He also acknowledged that "several people" had been killed in the unrest.
"One fell off a bridge, two died in car accidents and one was killed by a bullet," Radan said.
Referring to the person shot dead, he said: "As the police was not using firearms this [death] is suspicious and it is being investigated."
Opposition websites said there had been at least four deaths among the protesters in Tehran while another four died in a violent crackdown on opposition protests in the northwestern city of Tabriz.
"During clashes between security forces and protesters ... at least four protesters were killed in Tabriz and many others wounded," the Jaras website said.
There were also unconfirmed reports of fierce clashes in the city of Isfahan and Najafabad.
The Jaras website also said that protesters in Tehran had chanted angry slogans seeking revenge for those killed.
"We will kill those who killed our brothers," it quoted demonstrators as chanting.
Pictures linked on the Twitter microblogging site appeared to show a man with a wound to his head being carried away by opposition protesters.
The clashes came as the country's Shia Muslims marked Ashoura, a religious event commemorating the 7th century death of Prophet Muhammad's grandson.
Amateur video footage posted on the internet, said to be from the protest, showed protesters running away from riot police or Basij militias on motorbikes.
The opposition had urged people to gather in central Tehran on Sunday morning in defiance of warnings of a harsh crackdown on any protests during Ashoura.
Ghanbar Naderi, a journalist with the Iran Daily, an official government newspaper, criticised the protesters for choosing the day of Ashoura to stage demonstrations.
"This is the wrong place and the wrong time for the reformist camps to ask their supporters to get to the streets because this is a very important religious day for the whole of the nation"
Iran Daily journalist
"This is the wrong place and the wrong time for the reformist camps to ask their supporters to get to the streets because this is a very important religious day for the whole of the nation," he told Al Jazeera.
"If they are going to challenge the system now, they have no place among the ordinary citizens. People want to mark and commemorate the martyrdom of Imam Hussein and not their support of any political group or faction."
Sadegh Zibakalam, a professor at the University of Tehran, told Al Jazeera that the sheer number of people gathering in the street for religious commemorations would make it difficult for the police to keep control.
"It's very difficult for the police to prevent the crowds today because Ashoura is the most important day in Shia religion. Hundreds and thousands and millions of people come out in the street towards noon.
"It will be very difficult for the police to distinguish between genuine mourners and those who want to use the procession to register their protest against the government."
The latest protests came after violence broke out on Saturday when a speech by Mohammed Khatami, the former president, was cancelled.
Widespread protests have been held in Iran following the disputed presidential election on June 12.
Protests against the re-election of Mahmoud Ahmadinejad triggered deadly clashes between protesters, security forces and government-backed militia.
Opposition leaders Mir Hossein Mousavi and Mehdi Kharroubi have said the election was rigged.