"The interior ministry and other concerned organisations must take immediate action to investigate the cause of the incident," Khatami was quoted as saying in a condolence message carried by the student news agency ISNA on Tuesday.
The judiciary has been tasked with investigating the disaster, spokesman Jamal Karimi-Rad told state television.
The television listed other causes of the high death toll in the blaze on the eve of the Shia religious festival, Ashura, as a lack of fire safety equipment, the dilapidated structure of the 70-year-old mosque, and leaky heaters.
Police said that a stampede triggered by panic was to blame for the high death toll in Monday's disaster, whilst many worshippers had suffocated to death from the smoke.
"It was absolute panic ... a lot of people were hurt in rushing towards the exits," said a police commander.
The fire killed 60 people and 300
others were wounded
The blaze broke out as the faithful were packed for evening prayers inside the Ark mosque near Tehran's main bazaar, when panicked screams rang out from the women's section, state television reported.
"When I realised a fire had broken out in the women's section, I rushed to help my mother and sister. But my eight-year sister was trampled to death in the stampede," an unidentified young man told the state news agency IRNA.
At least 60 people perished and 300 others suffered burns, according to the latest toll on the television.
Media reports said the fire was probably caused by a heater brought into the mosque to protect worshippers from the bitter cold and which set a tent ablaze and spread flames like wildfire through the mosque's courtyard.