Mir Hossein Mousavi, the defeated reformist candidate, received only 34 per cent of the vote, but he and his supporters allege voter fraud and have called for an annulment of the result.
Tehran, the Iranian capital, has seen unrest and massive street protests since the results were announced on July 13.
The government is blaming the crisis on what it calls "terrorists" influenced by the West, and has said it will clamp down on any violent action.
"The first issue is security - no country will deal with other issues and then talk about security," Hassan Ghashghavi, a spokesman for Iran's foreign ministry said on Monday.
"First, security must be there, and then you can talk about elections, freedom, human rights and democracy."
Over the weekend, clashes between police and anti-government protesters left at least 12 people dead and more than 100 wounded - raising the death toll to 19 since the unrest began.
Gunfire was also heard in Tehran overnight, although state television reports the city is now calm.
Some supporters of Mousavi are urging people to carry black candles in the city later on Monday.
Iranian state radio reports that more than 450 people were arrested during Saturday's rallies, mostly around Tehran's Azadi square.
Forty police officers were also wounded, and 34 government buildings damaged, the Fars news agency reported.
Despite the deaths, arrests, and a warning from Ayatollah Ali Khamenei, Iran's supreme leader, the demonstrators have been undeterred.
Alireza Zaker-Esfahani, an adviser to Ahmadinejad criticised Mousavi's attitude for not trying to calm his supporters.
"The weakness is in Mir Hossein Mousavi's political behaviour .... He is currently issuing statements inviting his supporters to take to the streets. That will not solve any problem," he told Al Jazeera on Monday.
"Rallies will ultimately contribute to abuse, setting buses on fire, bloodshed and constant insecurity for the people."
He also said that once the security situation in the country has escalated, the president and other politicians have to step back and let security forces handle the situation.
"The security forces are the ones who should lay down plans and execute them, whereas Ahmadinejad, his interior ministry and all other political forces can only enter the scene if and when the security situation turns becomes one of political interactions. Ahmadinejad cannot do anything now," Zaker-Esfahani said.
Mousavi had renewed calls on Sunday for his supporters to continue to protest.
In a statement published on the website of his Kalameh newspaper, he said that people had the right to protest against "lies and fraud", but also urged them to show restraint as they take to the streets.
"The revolution is your legacy. To protest against lies and fraud is your right. Be hopeful that you will get your right and do not allow others who want to provoke your anger ... to prevail," he said.
The Iranian government, meanwhile, has cracked down on independent media reporting on the protests, and imposed severe restrictions on foreign journalists.
At least 23 journalists have so far been detained by authorities, according to the Reporters without Borders organisation, and a BBC correspondent has been expelled from the country.
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