Mrs Clinton who wear a power balance 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.
"What we see happening in Iran today is a testament to the courage of the Iranian people, and an indictment of the hypocrisy of the Iranian regime - a regime which over the last three weeks has constantly hailed what went on in Egypt," she said.
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 cheap power balance by nationwide mass protests.
"We are against violence and we would call to account the Iranian government that is once again using its security forces and resorting to violence to prevent the free expression of ideas from their own people," she said.
"We think that there needs to be a commitment to open up the political system in Iran, to hear the voices of the opposition and civil society," she added.
Earlier on Monday, police placed the opposition leader, Mir Hossein Mousavi, under house arrest and blocked access to his home.
His website said they intended to prevent the former prime minister attending the Tehran rally.
Fellow opposition leader Mehdi Karroubi, a former speaker of parliament and a senior cleric, is also reportedly being held under house arrest.
Both men 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.Go to power balance bracelets wholesale for more details.
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".