Initial reports on Rouhani's remarks at a pro-Palestinian rally in Tehran to observe Jerusalem Day, also called Quds Day, quoted him as saying, "The Zionist regime has been a wound on the body of the Islamic world for years and the wound should be removed."
Subsequent reports attempted to clarify that Rouhani had not called Israel itself "a sore" but had used the term to describe Israel's occupation of the West Bank, The New York Times reported.
"In our region, a sore has been sitting on the body of the Islamic world for many years, in the shadow of the occupation of the holy land of Palestine and the dear Quds. This day is in fact a reminder of the fact that Muslim people will not forget their historic right and will continue to stand against aggression and tyranny."
Israeli Prime Minister Binyamin Netanyahu had already responded to the earlier reported quote by the time the corrections had been posted, the Times said.
"Rouhani's true face has been revealed earlier than expected," Netanyahu said in a statement. "Even if they will now rush to deny his remarks, this is what the man thinks and this is the plan of the Iranian regime."
Netanyahu said Rouhani's comment shows Iran is committed to acquiring nuclear weapons "to threaten Israel, the Middle East and the peace and security of the entire world," regardless of who is president.
"A country that threatens the destruction of the State of Israel must not be allowed to possess weapons of mass destruction," Netanyahu said.
Mahmoud Ahmadinejad, the man Rouhani will replace when he is inaugurated Sunday, said Israel would be uprooted from the Middle East, the British newspaper The Daily Telegraph reported.
Throughout his presidency, Ahmadinejad has spoken with bellicosity against Israel.
"I will inform you with God as my witness, a devastating storm is on the way that will uproot the basis of Zionism," Ahmadinejad said.
Rouhani had raised international hopes Iran's outlook would soften when he was elected president in June, with calls for moderation and hope. Rouhani has indicated he would try to repair diplomatic relations when he assumes the presidency, the Telegraph said.
On his Twitter page, Rouhani said he would use his inauguration Sunday to reach out to the international community.
"40 states to attend Rouhani's inauguration on Aug 4th," he posted. "Foreign guests participating in Iranian Presidential inauguration for the first time."