A group of reformist clerics founded and led by Khatami said a referendum was essential to restore public confidence.
"As millions of Iranians have lost confidence in the electoral process, the Association of Combatant Clerics insist on the organisation of a referendum ... by independent bodies," the group said in a statement.
Under the Iranian constitution only Ayatollah Ali Khamenei, the country's supreme leader, can organise a referendum.
Khameini has backed the official results from the presidential election, which saw Ahmadinejad returned with a huge majority.
But his repeated calls on the opposition, including on Mir Hossein Mousavi, the defeated presidential candidate, to accept the poll outcome have gone unheeded.
Mousavi insists that the vote was rigged and says the government led by Ahmadinejad is "illegitimate".
On Monday, Mousavi demanded that scores of protesters detained following the poll be released immediately.
The election result triggered violent protests across Iran, resulting in the deaths of at least 20 people.
Speaking to the families of some of the activists and protesters held since the June 12 poll, Mousavi said that detaining people would not resolve the dispute over its outcome, reformist websites reported.
"Who believes these people, many of them prominent figures, would work with the foreigners and to endanger their country's interests?" he was quoted as saying.
"They should be immediately released."
Mousavi's remarks were published shortly after Khameini warned "Iran's elite" against harming the country's security.
"Anyone, no matter their rank or title, will be detested by the people if they lead our society towards insecurity," he said in a speech carried on state television.
"Our leaders must be vigilant. Any word or action which helps [the enemies] will be contrary to the interests of our people."