Khatami's proposal was reported by several reformist Web sites on Monday.
He said Iranians have lost their faith in the ruling political system following the June 12 election. The opposition charges that President Mahmoud Ahmadinejad won the election through mass fraud.
"Durability of order and continuation of the country's progress hinge on restoring public trust," Khatami, a popular reformist, said, according to the Web sites. "From the start, we said there is a legal way to regain that trust. I openly say now that the solution to get out of the current crisis is holding a referendum."
Iranian state radio reports that supreme leader Ayatollah Ali Khamenei told politicians to be careful in their stances on the country's postelection unrest, saying that disturbing security is "the biggest vice." Khamenei has declared the result of the elections as valid.
Khamenei also said that foreign enemies supported the unrest by broadcasting "procedures for rioting" through their media, according to Monday's state media report.
Under Iran's constitution, a referendum has to be ordered by Khamenei himself. All popular votes in Iran are monitored by an oversight body called the Guardian Council. Khatami, however, proposed that a neutral body, such as the Expediency Council, should monitor the proposed referendum instead.
Reformists have accused the Guardian Council of openly supporting Ahmadinejad in the election dispute.
The Expediency Council is a powerful clerical body that arbitrates disputes between the legislature and the government. It also advises Khamenei.
Opposition leader Mir Hossein Mousavi claims he won the June 12 election, saying official results showing a landslide victory for Ahmadinejad are fraudulent. Hundreds of thousands of Mousavi's supporters have staged street protests to denounce the results.
At least 20 protesters have since been killed and hundreds detained in clashes with security forces.