Tehran has seen mass demonstrations by all sides since the disputed election (see correction below)
US President Barack Obama is resisting pressure to side with Iran's opposition as mass protests continue over the nation's disputed presidential poll.
In a TV interview on Tuesday Mr Obama said there might not be much difference between the policies of President Ahmadinejad and rival Mir Hossein Mousavi.
Mr Mousavi's supporters have continued street protests despite the threat of government force and earlier bloodshed.
BBC correspondents in Tehran say the mood in the city is tense and angry.
Tough new restrictions have been imposed on foreign media in Iran.
But despite government attempts to control the flow of information out of the country, Iranians have been using the internet to send images and personal accounts of the protests around the world.
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
Mr Obama said he believed Iranian voices should be heard, although he added that he did not want to be seen to be "meddling".
"It is not productive, given the history of US and Iranian relations to be seen as meddling in Iranian elections," he said.
"But when I see violence directed at peaceful protesters, when I see peaceful dissent being suppressed
it is of concern to me and it is of concern to the American people."
Speaking later in the television interview, he downplayed the importance to the world of the struggle for power in Iran.
"The difference between Ahmadinejad and Mousavi in terms of their actual policies may not be as great as has been advertised," he said.
Earlier on Tuesday, the US state department said it had asked the social networking site Twitter to delay maintenance work so that Iranians could keep using it as a communications tool.
Result in question
The BBC's Justin Webb, in Washington, says Mr Obama is wary of the US becoming sucked into a protest movement in favour of Mr Mousavi, particularly as some intelligence reports suggest that Mr Ahmadinejad might have genuinely won the election.
Mr Obama has been under pressure from some conservative politicians in the US to openly support the protesters, who claim Mr Ahmadinejad's re-election is the product of vote rigging.
Republican John McCain, Mr Obama's defeated 2008 election rival, said: "He should speak out that this is a corrupt, fraud, sham of an election."
Iran's powerful Guardian Council says it is ready to recount some votes from the poll. A spokesman for the council, Abbas Ali Kadkhoda'i, told the state broadcaster Irin that the council had met representatives of the presidential candidates and would look into their allegations.
But opposition candidates have demanded a full re-run of the election.
President Ahmadinejad was declared the easy victor of the presidential poll on Saturday, with results giving him 63% of votes against 34% for Mr Mousavi.
Widespread anger at the result brought hundreds of thousands of Mr Mousavi's supporters on to the streets on Monday and eight protesters died when a rally ended in violence.
A witness told the BBC that Tuesday's rally in northern Tehran 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 the authorities.
Thousands of President Mahmoud Ahmadinejad's supporters staged a counter-rally in Vali Asr Square in central Tehran - some bussed in from the provinces, correspondents say.
A BBC correspondent in Tehran said that protesters also blocked roads with their cars, and police set up roadblocks to control gatherings of demonstrators.
As night fell, residents took to the roof-tops of their houses to shout protest messages across the city, a scene not witnessed since the final days of the Shah, our correspondent says.
Update 19 June 2009: an earlier version of our caption was incorrect. We wrongly stated that this was a pro-Mousavi rally when in fact it was a pro-Ahmadinejad rally.