But, Khamenei's warning fell on deaf ears of Mehdi Karoubi, one of the defeated candidates in the elections, who said that the new government was "illegitimate".
"I do not accept the result and therefore consider as illegitimate the new government. Because of the irregularities, the vote should be annulled," Karoubi's website quoted him as saying.
"Yasmin", a student protester told Al Jazeera that several hundred people had gathered near the parliament, but Mousavi was yet to show up.
She said the protesters were hiding in metro stations and pretending to be just passing by to hoodwink police deployed across the city in very large numbers.
Al Jazeera's Alireza Ronaghi said from Tehran that given the stringent security measures, staging rallies was going to be very difficult.
The protest rally was originally scheduled for 4pm (11:30 GMT), according to reports on social-networking sites and websites linked to the opposition.
At least 19 people have been killed in clashes with police and pro-government militia amid angry protests that broke out after Mousavi declared that the election had been rigged.
Mehdi Karroubi, who came in fourth in the poll, according to official results, has called for Iranians to hold ceremonies on Thursday to mourn those killed in the protests.
Although streets protests have diminished since police and pro-government militias used tear gas, batons and water cannon against protesters on Saturday, calls for further protests among supporters of Ahmadinejad's opponents have continued.
Nazenin Ansari, the diplomatic editor of the Kahylan newspaper, told Al Jazeera that the fall in numbers gathering to protest was understandable given the "degree of repression on the streets".
"Without a doubt, although there are not millions gathering on the streets because of the indiscriminate fire and repression, this is going to transform," she said.
"In provinces, where people were before gathering in universities, in recent days we are seeing people gathering in main squares."
Sadeq Mahsouli, Iran's interior minister, has accused the US Central Intelligence Agency (CIA) of helping those who have taken part in the protests.
"Many of the rioters were in contact with America, CIA and the MKO and are being fed by their financial resources," he was quoted as saying by the semi-official Fars news agency. The MKO (Mujahedeen-e-Khalq) is an exiled Iranian opposition group.
Mousavi, a former prime minister, and the two other candidates in the election have all filed complaints to the Guardian Council about alleged problems with the June 12 vote.
But on Wednesday, Mohsen Rezaie, the conservative candidate who finished third in the election, withdrew his objections.
"I see it as my responsibility to encourage myself and others to control the current situation," the official IRNA news agency reported Rezaie as saying in a letter to the Guardian Council.
"Therefore I announce that I'm withdrawing my submitted complaints," the former head of the Revolutionary Guard said.
Rezai had originally complained that he had won more votes than he had been credited with when the interior ministry declared the results.
"I think he wants to remain in the framework of the Islamic republic - the framework that conservative newspapers are trying to push Mousavi and Karroubi out of," Al Jazeera's Ronaghi said.
"Mohsen Rezaie intends to stay close to the core of the Islamic republic and show his allegiance to the supreme leader by obeying his call that the elections are over."
'No major fraud'
Despite Khamenei agreeing to extend the deadline for filing election complaints by five days, a spokesman for the Guardian Council said that there will not be a fresh vote.
"If a major breach occurs in an election, the Guardian Council may annul the votes that come out of a particular affected ballot box, polling station, district or city," Abbas Ali Kadkhodaei was quoted as saying by Press TV, an Iranian government-funded television station.
"Fortunately, in the recent presidential election, we found no witness of major fraud or breach in the election. Therefore, there is no possibility of an annulment taking place," he said.
Meanwhile, an aide to Mousavi said that the former prime minister's newspaper had been raided and 25 employees arrested.
Ali Reza Beheshti said that the raid took place on Monday evening as they were preparing to relaunch Kalemeh Sabz, or the Green Word.
The newspaper had been unavailable for more than a week.
Beheshti said: "Among those arrested on Monday were five or six administrative employees while the rest were journalists.
"The agents who came to the newspaper did not show a warrant."