Two demonstrators in Dorud in western Iran sustained gunshot wounds, a video posted on social media shows, and are reported to have died.
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".
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 gathered at Azadi square, BBC Persian reports. A senior Revolutionary Guards' figure in Tehran said the situation in the city was under control.
Demonstrators would be met with "the nation's iron fist" if they continued, Brigadier-General Esmail Kowsari told student news agency ISNA.
In Mashhad, in the north-east, protesters burned police motorcycles in a confrontation caught on video.
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