Khatami's proposal was reported by several reformist websites on Monday.
It is too early to say whether Khatami's call for a referendum would be adopted by authorities, but it constitutes the latest challenge to Ayatollah Ali Khamenei, Iran's supreme leader who has the last word on state matters. Khamenei has declared the results of the elections valid.
On Sunday, dozens of supporters of Iranian reformist leader Mir Hossein Mousavi gathered in a square in the southwest city of Shiraz in order to protest against the results of the presidential elections. Videos posted on the Internet showed the protestors chanting "death to the dictator".
Many of the rally's participants were activists in the election headquarters of Mousavi and the other reformist presidential candidate, Mehdi Karroubi.
During the rally, the reformist camp members held a ceremony in which they expressed their gratitude to the activists who took part in the wave of protests which swept Iran after the elections.
The ceremony, which was held in a local cultural center in Shiraz, was approved by the authorities, most likely after its organizers agreed not to make it public. Nonetheless, dozens of people arrived at the center.
According to various reports, there were no clashes between the participants and the security forces, and no protestors were arrested, the activists sang songs in support of the protest movement and its leader Mousavi.
Dudi Cohen contributed to this report