Defeated candidate Mir Hossein Mousavi repeated calls for the election to be annulled on the grounds it was rigged.
There were also reports of a bombing at the shrine of Ayatollah Khomeini. Two Iranian news agencies reported that the suicide bomber died and two people were injured in the bombing near the shrine of Ayatollah Khomeini, leader of the 1979 revolution.
There was no evidence to support the report, the BBC’s Jon Leyne says from Tehran.
The country’s supreme leader Ayatollah Khamenei had warned protesters on Friday not to continue their rallies, but correspondents say the warning appears to have made some protesters more determined.
It was unclear if political leaders had backed their supporters continuing to march.
In a letter to the electoral body, the 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, held on 12 June, was rigged months previously. Official results of the presidential poll gave President Mahmoud Ahmadinejad a resounding 63% of votes, compared to 34% for Mr Mousavi, his nearest rival.
In other developments:
Thousands of police, militia and secret policemen blocked access to Enghelab and Azadi squares, and protesters were throwing stones in surrounding streets. A BBC correspondent saw one man shot in a crowd and another with injuries from a razor-wielding secret policeman
About 3,000 protesters were reportedly gathered at Enghelab Square, according to Associated Press news agency. They chanted “Death to the dictator” and “Death to dictatorship”
One witness told Reuters news agency that protesters loyal to defeated candidate Mir Hossein Mousavi set fire to a building in southern Tehran used by backers of President Mahmoud Ahmadinejad .
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