In a highly spirited debate on national television Wednesday between Ahmadinejad and former Prime Minister Mir-Hossein Mousavi, Ahmadinejad launched into a tirade of accusations against Rafsanjani and former President Mohammad Khatami, both Mousavi supporters.
Ahmadinejad accused the Rafsanjani family of money-laundering and plotting with other state officials to oust the incumbent from office.
Mohammad Hashemi Rafsanjani, the former president's brother and former head of Islamic Republic of Iran Broadcasting, said his family would file their lawsuit against Ahmadinejad following the June 12 elections, the Iranian Press TV reports.
Meanwhile, Zahra Rahnavard, the wife of the former prime minister, told Press TV on Friday she would file a formal complaint against Ahmadinejad for accusing her of falsely obtaining her doctoral degree.
"If the president does not apologize within the next 24 hours, I will file a compliant against him," she said.
Ahmadinejad faces challenges in the June 12 contest from Mousavi, former military commander Mohsen Rezaei and former Parliamentary Speaker Mehdi Karroubi.
Mousavi has emerged as the top rival to Ahmadinejad, whose term expires in August.