The authorities announced tough new restrictions on foreign media, requiring journalists to obtain explicit permission before covering any story. Journalists have also been banned from attending or reporting on any unauthorised demonstration.
Our correspondent says they are the most sweeping restrictions he has ever encountered reporting anywhere.
The march was due to have taken place in Tehran's Vali Asr Square at the same time as a demonstration there by supporters of
Mahmoud Ahmadinejad.
VOTE RECOUNT
Jon Leyne Reporting from Tehran
The more I see this announcement about being willing to recount ballots, the more I think it is just a political ruse to try and wrong-foot the opposition. They have offered a recount, but they have not said who is going to carry it out. Maybe the same people who did the election count to start with.
In any case, the opposition says there were so many other irregularities, that a recount alone would not satisfy them. For example, many more ballot papers were issued than counted, they say. Some people did not get enough ballot papers so they could not vote in areas loyal to the opposition. Polling stations were closed early, and so on and so forth.
Thousands of the president's followers have converged there in a show of strength, cramming into tree-lined boulevards, some waving the national flag, as well as ones of orange, yellow and green.
'Missing ballots'
The Guardian Council - Iran's top legislative body - said votes would be recounted in areas contested by the losing candidates.
But a spokesman for the council told state television it would not annul the election - as moderate candidates have demanded.
The opposition says millions of ballots may have gone astray.
Monday's protest involved hundreds of thousands of people and was one of the largest since the Iranian revolution 30 years ago.
A report on state radio said "thugs" staged an attack at the end of the "illegal" rally as people were heading home "peacefully".
"Several thugs wanted to attack a military post and vandalise public property in the vicinity of Azadi Square," the radio said, referring to the site of the protest.
"Unfortunately seven people were killed and several others wounded in the incident."
Hospital officials later put the number of dead at eight.
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Supporters of President Ahmadinejad rally in Tehran on Tuesday
Dozens of people have been arrested since the protests began. Mohammad Ali Abtahi, a close aide of ex-President Mohammad Khatami, was detained at his home in Tehran on Tuesday.
Those detained also include prominent journalist and academic Ahmad Zeidabadi. His wife says he was picked up in the middle of the night on Saturday.
GUARDIAN COUNCIL
Iran's most powerful body, currently controlled by conservatives
Includes six theologians picked by Supreme Leader and six jurists approved by parliament
Half the members change every three years
Approves bills passed by parliament and can veto them if deemed inconsistent with the constitution or Islamic law
The council can also bar candidates from standing in elections
"There is no explanation from the authorities about why he was arrested or where he is," she told the BBC.
Meanwhile, Iranian state television said the "main agents" behind the unrest had been detained, and guns and explosives seized.
There are reports of fresh demonstrations at Tehran University - one of the main centres of tension in recent days. About 120 university lecturers have resigned.
The powerful Speaker of parliament, Ali Larijani, has condemned an attack by police and militia on a student dormitory.
Iranian media quoted him as saying: "The interior minister is responsible in this regard."
Unrest has been reported in other parts of Iran. One of Mr Mousavi's websites said a student had died on Monday in clashes with hardliners in the southern city of Shiraz.
Foreign concern
Our correspondent says the authorities appear to be weakening in their support for President Ahmadinejad.
Jon Leyne in Iran: 'A huge battle behind scenes'
The country's supreme leader, Ayatollah Ali Khamenei, has ordered an inquiry into the allegations of vote-rigging.
The authorities' handling of the protests has drawn international criticism.
EU foreign ministers expressed "serious concern" and called for an inquiry into the conduct of the election.
US President Barack Obama said he was "deeply troubled" by the violence in Iran.
Meanwhile, President Ahmadinejad arrived in Russia on Tuesday.
He told a regional summit that the "age of empires" had ended, but made no mention of the protests.
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