Rafsanjani was a close confidant of Khamenei for much of the 1980s and 1990s but the pair fell out when the former lost to Ahmadinejad in the 2005 presidential vote.
Talk of sanctions is seen as an indirect criticism of Khamenei for his reluctance to compromise over Tehran's nuclear dossier.
Although Rafsanjani and Mashaei are rivals with complete different political allegiances, they are both loathed by the supporters of Khamenei for allegedly attempting to undermine his power.
The TV aired a brief footage of Khamenei just ahead of the surgery in which he asked people to pray for him.
Supporters of Khamenei have accused Mashaei of putting Iran ahead of Islam and not showing enough loyalty to the supreme leader.
His daughter is married to Mojtaba Khamenei, one of the Supreme Leader's sons.
Supporters of Khamenei have accused Mashaei of attempting to undermine the supremacy of his leadership by advocating nationalism, putting Iran ahead of Islam and favouring greater cultural openness.
In the light of Khamenei's support, opponents of the deal have kept quiet.
Hence Brigadier General Mohammad Reza Naqdi, the Basij commander, was appointed in 2009 "by command" of Khamenei at the suggestion of Major General Mohammad Ali Jafari, the IRGC commander.
