BBC Tehran correspondent Jon Leyne, reporting from London, says the government's immediate response to the latest confrontation has been to arrest senior opposition figures, as it did after protests against the disputed presidential elections in June.
The authorities are blaming troublemakers for the violence, our correspondent says, with the police suggesting that protesters may have shot each other.
Among those reported arrested on Monday were opposition politician Ebrahim Yazdi, a foreign minister after the 1979 revolution and now leader of the Freedom Movement of Iran, his nephew, Lily Tavasoli.
The Parlemannews website reported that three aides to Mir Hossein Mousavi had been arrested.
It also named two aides to reformist former President Mohammad Khatami as being among those rounded up by the authorities.
Mousavi Tebrizi, a senior cleric from the holy city of Qom who is close to Mr Mousavi, is also reported to have been arrested, as is human-rights campaigner and journalist Emeddin Baghi.
Iranian security forces have been on alert since influential dissident cleric Grand Ayatollah Hoseyn Ali Montazeri died a week ago aged 87.
His funeral attracted tens of thousands of pro-reform supporters, many of whom shouted anti-government slogans.
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