Footage claiming to show a rally near Tehran's Shiroudi stadium on Monday
United Nations Secretary General Ban Ki-moon has called for an immediate end to arrests and the threat and use of violence by authorities in Iran.
He urged them to respect fundamental civil rights, "especially the freedom of assembly and expression".
His comments came as there were further clashes in the capital Tehran.
Iran's legislative body, the Guardian Council, said there were no major polling irregularities in the 12 June election and ruled out an annulment.
The ruling was reported by state television on Tuesday.
A spokesman for the Guardian Council, Abbas Ali Kadkhodaei, was quoted by the English-language Press TV as saying the council had found "no major fraud or breach in the election".
The ruling came after a rally on Monday had taken place despite warnings against such gatherings by the Revolutionary Guards.
A spokesman for Mr Ban said he had been following the situation in Iran with "growing concern" and was dismayed by the post-election violence, particularly the use of force against civilians.
A statement said: "He calls on the authorities to respect fundamental civil and political rights, especially the freedom of expression, freedom of assembly and freedom of information."
He called on Iran's government and opposition to resolve their differences peacefully through dialogue and legal means.
"He urges an immediate stop to the arrests, threats and use of force. The secretary general reiterates his hope that the democratic will of the people of Iran will be fully respected," the statement read.
Some 1,000 people gathered in Haft-e Tir Square despite the warning from Iran's Revolutionary Guards against holding unapproved rallies.
Basij militiamen wielding clubs were brought in to reinforce the police.
The guards, an elite armed force, vowed to crack down on new street protests over the presidential election results.
On Friday, Ayatollah Ali Khamenei banned protests, prompting street violence in which at least 10 people died.
Severe reporting restrictions placed on the BBC and other foreign media in Iran mean protest reports cannot be verified independently.
Clubs and tear gas
Eyewitnesses said hundreds of riot police were used to drive the protesters from the square on Monday.
BBC Persian TV received an e-mail from one person saying: "There are lots of people but they are scattered, and lots of police guards. They are firing bullets in the air and using tear gas against the crowds."
The Revolutionary Guards have close ties to the country's supreme leader.
Video has emerged of Iranian police making arrests on Saturday
In a statement posted on their website, they said their troops would break up street protests and force protesters from the streets.
"Be prepared for a resolution and revolutionary confrontation with the guards, Basij and other security forces and disciplinary forces," they said.
"The guards will firmly confront in a revolutionary way rioters and those who violate the law."
The Basij militia was involved in quelling earlier protests during more than a week of demonstrations against the re-election of President Mahmoud Ahmadinejad.
'No memorial service'
Meanwhile, the fiance of Neda Agha-Soltan, the young woman whose violent death during clashes in Tehran on Saturday was recorded on video and uploaded to the internet, has described the events leading up to her shooting in an interview for BBC Persian TV.
She had been sitting with her music teacher in a car, stuck in traffic, when she decided to get out because of the heat.
The authorities are aware that everybody in Iran and throughout the whole world knows about her story
"She got out of the car for just for a few minutes [and] that's when she was shot dead," said Caspian Makan.
Mr Makan quoted eyewitnesses as saying she appeared to have been targeted deliberately by "paramilitaries in civilian clothing".
He added that officials had prevented mourners holding a memorial service at a mosque on Monday.
"The authorities are aware that everybody in Iran and throughout the whole world knows about her story," he told the BBC. "They were afraid that lots of people could turn up."
Election results show Mr Ahmadinejad won the 12 June election by a landslide, taking 63% of the vote, almost double that of Mir Hossein Mousavi, his nearest rival.
The Guardian Council, which oversees the electoral process, said it had found some evidence of voting irregularities but the number had "no effect on the result of the elections".
An independent British analysis of the disputed election results has found irregularities in the reported turnout, as well as "implausible" swings in the vote in favour of Mr Ahmadinejad.
Analysts from St Andrew's University and the Chatham House think-tank said votes in favour of Mr Ahmadinejad in a third of the provinces would have required an "unlikely scenario" of voting patterns.
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