But opposition demands for annulling the results have been rejected by the election authorities and Ahmadinejad, re-elected for a second term, on Thursday accused Western powers of interfering in last month's vote.
Ahmadinejad also criticised Rafsanjani, an influential cleric who was president in the 1990s, over his support for Mousavi.
Rafsanjani will lead the prayers after a two-month absence. Some of his relatives, including his daughter Faezeh, were arrested briefly for taking part in pro-Mousavi rallies.
He's one of Iran's wealthiest and most powerful men, and one of only four Tehran clerics allowed to adress the nation during the weekly Friday prayers.
Analysts say his speech may either quell or reignite the worst unrest in the Islamic Republic in the last 30 years.
Rafsanjani heads two of the regime’s most powerful bodies: the Expediency Council - which settles disputes over laws between the parliament and the Guardian Council, and the Assembly of Experts – which has the power to appoint, supervise and in theory dismiss the Supreme Leader.
On Tuesday, Iran's Etemad newspaper said Mousavi's reformist ally, Mohammad Khatami, a former president of Iran, would also attend the prayers.
Mehdi Karroubi, another defeated candidate, will also attend, his party's website said.
The election strained ties between Iran and Western nations, already at odds over Tehran's nuclear programme.
Gholamhossein Mohseni-Ejei, Iran's intelligence minister, told the Fars news agency: "The vigilant Iranian nation must be aware that tomorrow's sermon should not turn into an arena for undesirable scenes."