Khatami, whose 1997-2005 presidency saw a thaw in the Islamic republic's relations with the West, hit out at the conduct of the June 12 vote that saw his hard-line successor Mahmoud Ahmadinejad returned to power.
He expressed concern that "public confidence in the system has been damaged," the ILNA news agency reported.
Khatami said calls by another former president Akbar Hashemi Rafsanjani for a consensus between reformers and conservatives on resolving the crisis were the "minimum requirement for getting out of the current situation."
The ex-president also demanded the release of everyone detained during the wave of protests across the country since the election, which the opposition charges was marred by widespread fraud.
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.
It did not elaborate.
Under the Iranian constitution only the supreme leader Ayatollah Ali Khamenei can organise a referendum.
The clerical body said it supported Rafsanjani, a powerful cleric who made a hard-hitting address on Friday criticising the election and the subsequent crackdown on the opposition.
In his first comments since the vote, Rafsanjani said it had broken the trust of the people, and called for the release of hundreds of people detained in the unrest.
