But there were reports of small groups of opposition supporters gathering nonetheless.
The opposition march had been due to take place in Tehran's Vali Asr Square at the same time as a demonstration there by supporters of Mr Ahmadinejad.
Thousands of the president's followers have converged there, some waving the national flag.
The new restrictions on foreign media require journalists to obtain explicit permission before leaving the office to cover any story.
Journalists have also been banned from attending or reporting on any "unauthorised" demonstration - and it is unclear which if any of the protests are formally authorised.
Jon Leyne Reporting from Tehran
I really get the impression that the authorities are swinging back and forth between different policies. There is definitely indecision in the leadership, maybe even a power struggle there.
Because, frankly, they are simply witnessing the completely unexpected - nobody expected to see possibly millions of people out on Monday, in defiance of all the threats.
The government is so used to putting threats out and frightening people away from demonstrating. And suddenly this defiance has completely wrong-footed them. And it scared them, because this is exactly the way they came to power in 1979.
Press cards have been declared invalid.
Our correspondent says they are the most sweeping restrictions he has ever encountered reporting anywhere.
He says the clampdown comes amid surprise and fear among authorities at the show of defiance by opposition supporters who attended Monday's huge illegal rally, insisting the vote was rigged.
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.
Hospital officials said eight people died at the end of Monday's protest, in violence which a report on state radio blamed on "thugs".
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.
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.
The authorities' handling of the protests has drawn international criticism.
The BBC's Jon Leyne in Tehran says his movements have been restricted
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.
But the Iranian authorities have bristled over the criticism. On Tuesday the Iranian foreign ministry summoned the Czech charge' d'affaires in Tehran to complain over the EU's "rude and interfering" remarks.
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.
Are you in Iran? What do you think of the current situation? If you have any information you would like to share with the BBC you can do so using the form below:
Send your pictures and video to email@example.com or text them to +44 7725 100 100. If you have a large file you can upload here.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.