The comments by Ali Akbar Velayati, foreign policy adviser to Iran's supreme leader Ayatollah Ali Khamenei, came after it was announced that the April 5 vote winner will be named Saturday, two days later than planned.
With half the ballots from the election to succeed Afghan President Hamid Karzai counted, former foreign minister Abdullah Abdullah is ahead of his main rival Ashraf Ghani.
But serious fraud concerns are being probed to try and ensure a cleaner election than in 2009, when Karzai retained power in a poll marred by rampant cheating.
Afghan officials have vowed to sift out fake votes.
However, Velayati, who was Iran's foreign minister between 1981 and 1997, said the poll had been well-managed.
"The Afghanistan presidential election was held very fairly and with complete security," he told Iran's official IRNA news agency.
"It was part of other positive developments in that country," he added.
Iran has the second-highest population of Afghan refugees after Pakistan, with 840,000 officially registered, according to the United Nations.
Iranian authorities say a further one million Afghan refugees are in the country illegally.
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