Fahimi made her call in an open letter posted on the opposition "Kalame" website.
"Mr. Khatami, we lost our children on the path to reach independence, freedom and an honorable life," she wrote. "Their blood was innocently spilled on the asphalt of the streets. They wanted change and reforms to reach their goal. You have to feel responsible once more, and enter the scene, and do not allow the blood of these young people and the martyrs of the [Iran-Iraq] war to be plundered."
She added that Khatami should not turn the hopes of many into disappointment.
Fahimi has earned the respect of many with her outspokenness and her courage, becoming one of the heroes of Iran's opposition Green Movement, which has effectively been silenced by the authorities who have put its leaders under house arrest and pressured supporters through threats, arrests and imprisonment.
Her letter adds weight to mounting calls for Khatami to run in the upcoming vote.
Khatami has been publicly silent in the face of the increasing demands for him to stand in the presidential election, the first since the 2009 vote, which precipitated one of Iran's worst political crises.
(To read a profile of Parvin Fahimi click here)