"I don't expect someone who considers himself to be originally from Africa and a member of the oppressed black race in America to repeat what (George W.) Bush has to say," Rafsanjani said in a sermon on state radio.
In an interview broadcast on Sunday, Obama vowed "tough but direct diplomacy" with Iran, offering incentives along with the threat of tougher sanctions over its atomic programme.
During his term, Bush spearheaded the international campaign against Iran's atomic drive which the United States fears could be a cover for ambitions to build nuclear weapons, allegations denied by Tehran.
The outgoing US president once famously branded Iran as part of an "axis of evil" and never ruled out military action over its nuclear work.
"I advise (Obama)… we don't want your incentives and your punishments will not stop us either," he said in a speech marking the Muslim Feast of the Sacrifice or Eid al-Adha.
"It's better for you to be reasonable and not to deprive Iran of its rights."
The UN Security Council has repeatedly demanded that Iran freeze its uranium enrichment work, the process which makes nuclear fuel as well as the fissile core of an atom bomb, but Tehran has refused.
