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
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