But Ahmadinejad has said that the result proved he has popular support.
"The election result confirmed the work of the ninth government which was based on honesty and service to the people," he said on Wednesday in a statement to Iran's ISNA news agency.
Violence on tape
Despite the restrictions placed by the government on the media, violent scenes of police beating Mousavi supporters taken on mobile phones have been broadcast on news bulletins across the world.
The Revolutionary Guard has warned the country's online media it will face legal action if it "creates tensions".
Within the country, mobile phone text services have been down since the election. There is no access to Facebook, Twitter, or YouTube.
The interior ministry has ordered an investigation into an attack on university students in which it is claimed four people were killed.
Anoushaka Maraslian, a Middle East analyst in London, told Al Jazeera: "University cities in Iran have always been very active in political dissent.
"That's the concern of the elders; that's the concern of the Guardian Council, and that's why they're making conessions, because they realise that young Iranians are leading the protests ... with parallels to [the revolution in] 1979."
At least seven people have been killed in recent clashes between the authorities and the opposition movement, according to state media reports, while hundreds more are thought to have been injured.
For its part, the foreign ministry summoned the Swiss ambassador, who represents US interests in Tehran, on Wednesday to protest at "interventionist" US statements on Iran's election.
Obama told CNBC there appeared to be little difference in policy between Ahmadinejad and Mousavi.
"Either way we are going to be dealing with an Iranian regime that has historically been hostile to the United States," he said.
Mousavi has called on his supporters to hold peaceful demonstrations or gather in mosques on Thursday in solidarity with people killed or hurt in the post-election unrest.
"In the course of the past days and as a consequence of illegal and violent encounters with [people protesting] against the outcome of the presidential election, a number of our countrymen were wounded or martyred," Mousavi said on his website.
"I ask the people to express their solidarity with the families .... by coming together in mosques or taking part in peaceful demonstrations."
The announcement of the rallies came as news emerged that two prominent reformists allied to Mousavi had been arrested by the Iranian authorities.
Hamid Reza Jalaipour, a sociologist, was arrested at his home on Wednesday morning, Issa Saharkhiz, a colleague, told the AFP news agency.
Saeed Laylaz, a political and economic analyst, was also arrested at his home by four officials, a family member said.
Jalaipour and Laylaz are also prominent journalists.
|Iranian police have badly beaten some protesters at the opposition rallies [AFP]
Several reformists have been arrested by the Iranian authorities since the protests against the presidential election results began.
Foreign media reporters have been banned from covering rallies by those opposed to the result of the vote.
With Iranians relying on social networking sites and YouTube to share information, the Revolutionary Guard, an elite military force, warned users on Wednesday that they would face legal action if their uploads "create tension".
Alireza Ronaghi, Al Jazeera's correspondent in Tehran, said the move against websites and blogging by the Guard was beyond their remit.
"Their move to crack down on websites and blogs is against their constitutional rights, but they see it as things spreading out of hand, so they feel it necessary to intervene at this point," he said.
"It is obvious that the Revolutionary Guard does not see itself as a pure military organisation. They been telling the media and activists that the Revolutionary Guard was founded as a political and military foundation of the Islamic Republic, so they see it as appropriate to enter politics whenever they deem fit.
Tens of thousands of pro- and anti-government demonstrators held rival rallies in Tehran on Tuesday, despite calls by Mousaavi to exercise restraint for fear of provoking further clashes.
Thousands of people gathered at a government-organised rally in Tehran's central Vali Asr square in support of Ahmadinejad while a similar-sized demonstration was held in the north of the city by those loyal to the opposition.
Sadegh Zibakalam, an Iranian political analyst, said that the government had arranged its protest on Tuesday as a response to the opposition movement.
"The government doesn't want to appear as being too soft - that's why they called this rally today and asked its supporters to come to the square where Mousavi's supporters had decided to gather," he told Al Jazeera.
"By arranging these crowds, the government is making two points. It wants to demonstrate that it is firm in dealing with this crisis, [and] on the other hand they have been called [on] by the pro-government crowd to crack down."
The rallies came just hours after the Guardian Council, Iran's most senior legislative body, said it could order a partial vote recount, provided it finds irregularities.
The council ruled out annulling the disputed poll, the key demand of the opposition.