Mustafa Moin's campaign said in a statement on Monday that the first round of the presidential election was not free and fair.
"Since there were numerous reports of rigged votes and counting, we have filed a complaint, and in addition we request the postponement of the second round of the election until all the complaints from all candidates have been answered," it said.
The statement was addressed to the election supervisory arm of the Guardians Council, an unelected political watchdog that reformers have alleged was engaged in election irregularities.
Three of the seven candidates who stood in the first round of the election on Friday have complained of irregularities they say were aimed at propelling Tehran's mayor Mahmood Ahmadinejad into a runoff against cleric Akbar Rafsanjani.
Rafsanjani and cleric Mehdi Karoubi added their voices to Moin's by making public allegations of dirty tricks.
Two newspapers - Aftab and Eghbal - were closed on Monday for publishing their claims of vote rigging.
Election officials say the voter
identity checks were thorough
Commenting on the media bans, government official Issa Saharkiz said: "We do not know [yet] if this measure only applies to today's issue or if it is a more long-term ban."
Nevertheless, breaking a silence he has conspicuously maintained since the vote, Rafsanjani called on Iranians to back him in the runoff against extremists who he said had "tarnished" the poll.
"The Islamic revolution is at a difficult crossroads, facing domestic and foreign threats and adventurism," he said.
Centrist cleric Karoubi, who came third in the poll, has asked Iran's supreme leader Ali Khamenei to prevent "illegal intervention" by the Revolutionary Guards and the Guardians Council in the elections.
"I ask you to prevent a section of the Revolutionary Guards and Basij from engaging in political activities," said Karoubi, who resigned from all of his posts in the government.
Meanwhile, Iranian officials in the Guardian Council have said they will authorise the recount of a random selection of 100 ballot boxes.
"The Guardians Council, despite the fact that it has not received any complaints from the candidates of breaches in the prescribed time, will recount to produce a more accurate result," state television reported.
It said the recount had to be completed by 6pm on Monday, so the second round of the election could go ahead as scheduled next Friday.