Two demonstrators in Dorud in western Iran have sustained gunshot wounds, a video posted on social media and verified by BBC Persian shows.
Videos filmed elsewhere in the country show protesters setting fire to a police vehicles and there are reports of attacks on government buildings.
It is the biggest display of dissent since huge pro-reform rallies in 2009.
Demonstrators have ignored a warning by Iran's interior minister to avoid "illegal gatherings".
There are reports that the two protesters who were shot in Dorud have died. Much of the information about what is occurring is emerging on social media, making it difficult to confirm anything.
In the town of Abhar in northern Iran, demonstrators have set fire to large banners bearing the picture of Iran's Supreme Leader Ayatollah Ali Khamenei.
Meanwhile in Arak in central Iran, protesters have reportedly set fire to the local headquarters of the pro-government Basij militia.
In the capital Tehran, large numbers of protesters are converging on Azadi square, BBC Persian reports, with many police and security forces appearing to have withdrawn.
In Mashhad, in the north-east, protesters burned a police motorcycle in a confrontation caught on video.
There are also numerous reports of people losing internet access on their mobile phones.
In Kermanshah, western Iran, a demonstrator called Makan told BBC Persian that protesters were beaten up "but we couldn't tell if it was the police or the Basij militia".
"I'm not protesting against President Rouhani - and yes he needs to improve the economy - but it's the system that is rotten," he said. "It's the Islamic Republic and its institutions that need reform."
Earlier, protesters at Tehran University called for Ayatollah Khamenei to step down and there were clashes with police.
Thousands of pro-government demonstrators turned out earlier on Saturday for big rallies, organised in advance to mark the eighth anniversary of the suppression of the 2009 street protests.