Members of Iran's parliament have called for opposition leaders Mir Hossein Mousavi and Mehdi Karroubi to be tried and executed.
Some 50 conservative MPs marched through parliament's main hall on Tuesday, chanting "Death to Mousavi, death to Karroubi", shown on state TV.
Thousands of opposition supporters had protested in Iran's capital on Monday.
One person was reportedly shot dead in the violent clashes between protesters and security forces in central Tehran.
The BBC received reports of banned demonstrations in other Iranian cities, including Isfahan, Mashhad and Shiraz.
In the capital, dozens were detained, and opposition leaders including Mr Mousavi and Mr Karroubi were placed under house arrest.
Police blocked access to Mr Mousavi's home in what the former prime minister's website said was intended to prevent him attending the Tehran rally, which was lauded by the US administration.
Both he and Mr Karroubi - a former speaker of parliament and a senior cleric - disputed the re-election of President Mahmoud Ahmadinejad in June 2009, which triggered protests that drew the largest crowds in Iran since the Islamic Revolution in 1979.
The authorities responded by launching a brutal crackdown.
'Corrupt on earth'?
In a statement carried by the official IRNA news agency, conservative parliamentarians said: "Mehdi Karroubi and Mir Hossein Mousavi are corrupts on earth and should be tried."
The charge "corrupt on earth" has been levelled at political dissidents in the past and carries the death penalty in Iran.
Earlier, thousands of opposition supporters had gathered at Tehran's Azadi Square in solidarity with the popular uprisings in Tunisia and Egypt, in their first major show of dissent December 2009, when eight people were killed.
They chanted: "Death to dictators."
But the BBC's Mohsen Asgari, who was at the rally, says it was not long before riot police fired tear gas, while men on motorbikes charged the crowd with batons.
At least three protesters were wounded by bullets, with dozens of others taken to hospital as a result of the beatings, witnesses said.
Iran's semi-official Fars news agency reported that one person was shot dead by protesters and several others wounded.
Tehran's police chief, Ahmad Reza Radan, blamed the opposition leaders for instigating the protests.
"In one spot of the town in the western part of Tehran, about 150 people rallied and set some rubbish bins on fire," he said. "They were confronted by police and security forces and some of them were arrested.
"Unfortunately, some police and security personnel were shot by them and nine security forces men and some other people were wounded in this incident."
US Secretary of State Hillary Clinton said the US "very clearly and directly" supported the protesters.
She said they deserved to have "the same rights that they saw being played out in Egypt" and that Iran had to "open up" its political system.
Mrs Clinton said the US had the same message for the Iranian authorities as it did for those in Egypt, where President Hosni Mubarak was forced to step down after 29 years in power by nationwide mass protests.
The opposition says more than 80 of its supporters were killed over the following six months, a figure the government disputes. Several have been sentenced to death, and dozens jailed.
Although Iran's establishment supported the Egyptian and Tunisian protests, describing them as an "Islamic awakening" inspired by the Islamic Revolution, it said the opposition rallies were a "political move".
