| BBC update |
The opposition rally went ahead despite an official offer of a partial recount of the poll, which returned Mr Ahmadinejad to power.
Tough new restrictions have been imposed on foreign media reporting. The curbs came amid apparent surprise and concern among the authorities at the scale of popular defiance over Friday's official election results, correspondents say.
The powerful Guardian Council says it is ready to recount some votes from the poll, in a move backed by Supreme Leader Ayatollah Ali Khamenei. But opposition candidates have demanded a full re-run of the election.
A witness told the BBC that Tuesday's rally was even bigger than Monday's - though this cannot be independently confirmed - and the state Press TV also described it as large. Witnesses described demonstrators walking in near silence towards state TV headquarters - apparently anxious not to be depicted as hooligans by authorities.
The latest opposition rally comes despite a Mousavi spokesman urging supporters not to take part in another demonstration on Tuesday, amid fears of new violence.
The authorities have imposed tough new restrictions on foreign journalists operating in Tehran - the most sweeping restrictions our correspondent in Tehran, Jon Leyne, says he has ever faced. They must now 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.
Some telephone, SMS and internet services have also been restricted, prompting some protesters to turn to the internet messaging service Twitter to communicate. The importance of such new means of communication was highlighted by a US official on Tuesday. The official said the state department contacted Twitter over the weekend to urge it to delay a planned upgrade that could have cut daytime service to Iranians.