Clinton expresses US support for Iran protesters
Mrs Clinton 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.
One person was reportedly shot dead in the violent clashes between protesters and security forces in central Tehran.
Dozens were detained, and opposition leaders were placed under house arrest.
The BBC received reports of banned demonstrations in other Iranian cities, including Isfahan, Mashhad and Shiraz.
'Hypocrisy'
In their first major show of dissent December 2009, when eight people were killed, thousands of opposition supporters gathered at Tehran's Azadi Square on Monday in solidarity with the popular uprisings in Tunisia and Egypt.
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.
Witnesses told the Associated Press new agency that at least three protesters had been wounded by bullets, with dozens of others taken to hospital as a result of the beatings.
Iran's semi-official Fars news agency meanwhile reported that one person was shot dead by protesters and several others wounded.
Opposition websites said hundreds of people were arrested. There has been no official confirmation.
As night fell, hundreds of riot police remained on the streets of the capital.
Later in Washington, Mrs Clinton told reporters that the US administration "very clearly and directly" supports the protesters; Kazinform cites BBC News.
See www.bbc.co.uk for full version