The former President's aide told newsmen that Hasehmi had died at the hospital in Tehran.
State run Press TV said Rafsanjani, 82, died from a heart attack despite efforts by doctors to save him.
Rafsanjani was an influential figure in Iran, and headed the Expediency Council, a body which is intended to resolve disputes between the parliament and the Guardian Council.
Tasnim news agency also quoted his relative and aide Hossein Marashi as saying that Hasehmi had died at the hospital in Tehran.
The cleric was one of the architects of the Islamic Revolution that deposed the shah, Mohammad Reza Pahlavi, in 1979 and established a religious state.
He served as president between 1989 and 1997.