Former parliamentary speaker and unsuccessful first-round candidate Mehdi Karoubi had demanded a recount of the 17 June ballot.
Conservative Mahmud Ahmadinejad won the vote. He is set to succeed Khatami on 3 August.
A recount must first be authorized by the Guardians Council, which has the final say over the election's outcome and dismissed allegations of widespread fraud after the first round of voting.
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