Iranians send video footage of protests to the BBC
US President Barack Obama has warned Iran to stop all "violence and unjust action against its own people", after a day of protests over last week's vote.
Witnesses said security forces used batons and live ammunition in clashes with protesters, who had gathered in defiance of the country's leader.
Mr Obama urged Iran's leaders to "govern through consent, not coercion".
Defeated candidate Mir Hossein Mousavi repeated calls for the election to be annulled on the grounds it was rigged.
Mr Obama, in a statement from the White House on Saturday, said: "The universal rights to assembly and free speech must be respected, and the United States stands with all who seek to exercise those rights.
"The Iranian people will ultimately judge the actions of their own government."
Republicans critics of the administration have accused Mr Obama of not being outspoken enough in his condemnation of the Iranian government.
But the BBC's Jon Donnison in Washington says the president is treading a fine line - he does not want to be seen to be interfering, which could stir up anti-American sentiment within Iran and work against the protesters.
On Friday, after a week of unrest since the 12 June re-election of President Mahmoud Ahmadinejad, Iran's Supreme Leader Ayatollah Ali Khamenei warned protesters not to continue their rallies.
But thousands attempted to gather at Enghelab and Azadi squares in the centre of the capital on Saturday.
The two squares were blocked by police, and large groups of protesters were dispersed before regrouping into smaller clusters, witnesses said.
It was unclear if Iranian political leaders had backed the latest rallies.
Curbs on media
A BBC reporter said he saw one man shot and others injured amid fighting, with streets littered with burning debris.
Foreign news organisations - including the BBC - have been subjected to strict controls preventing reporters from leaving their offices.
As night fell, protesters could be heard shouting Allahu Akhbar (God is Great) from rooftops as they have done on previous nights.
In a letter to Iran's powerful Guardian Council, Mr Mousavi, who had not made a public comment for two days, reiterated his calls for the election to be declared void.
He alleged the vote was rigged months previously.
Official results of the presidential poll gave President Ahmadinejad a resounding 63% of votes, compared with 34% for Mr Mousavi, his nearest rival.
Analysts say the street protests are a challenge to ruling authorities, unprecedented since the Islamic revolution of 1979.
Mr Mousavi, along with fellow challengers Mehdi Karroubi and Mohsen Rezai, had been expected to discuss more than 600 objections they had filed complaining about the poll with the Guardian Council on Saturday
But neither Mr Mousavi nor Mr Karroubi attended the meeting.
State TV quoted the Guardian Council as saying it was "ready" to recount a randomly selected 10% of ballot boxes.
It had previously offered a partial recount of disputed ballots from the election, rather than the full re-run of the election demanded by protesters.
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