"Any crime that happens in history against humanity, including the crime that the Nazis committed toward the Jews, as well as non-Jewish people, is reprehensible and condemnable, as far as we are concerned," Rouhani told CNN in an interview conducted Tuesday and broadcast Wednesday (http://www.youtube.com/watch?v=_uZXXgm4cv8).
"Whatever criminality they committed against the Jews, we condemn, because genocide -- the taking of the human life -- is condemnable," he said. "And it makes no difference whether that life is a Jewish life, a Christian or a Muslim or what -- for us it's the same."
He said his comments were also supported by Islam.
At the same time, Rouhani said systematic, state-sponsored murder by Nazi Germany did not give Israel, without referring to Israel by name, a right to "usurp the land of another group and occupy it."
"This too is an act that should be condemned, in our view," he said. "There should be an even-handed discussion of this."
Rouhani's condemnation of the Holocaust, even with his caveat, was a marked departure from statements made by his Holocaust-denying predecessor, Mahmoud Ahmadinejad, although some critics said they were not satisfied since Rouhani did not flatly renounce Holocaust denial.
Iran's Fars News Agency, run by the conservative Revolutionary Guards, later accused CNN of fabricating Rouhani's response to the Holocaust question.
It published the text of Rouhani's remarks in Persian and compared the news agency's English translation of his words with CNN's.
Three weeks ago, Fars denied Rouhani sent a New Year's Rosh Hashana greeting to Jews around the world in a Twitter message.
The Sept. 4 message on Rouhani's official English-language account said, "As the sun is about to set here in #Tehran I wish all Jews, especially Iranian Jews, a blessed Rosh Hashanah."
In his CNN interview, Rouhani said Jews and other religious minorities were free to worship in Iran.
Judaism is one of the oldest religions practiced in Iran, dating from biblical times. The biblical books of Isaiah, Daniel, Ezra, Nehemiah, Chronicles and Esther contain references to Jewish life and experiences in Persia, Iran's earlier name.
Rouhani also sent greetings twice to Americans -- in Persian at the start of the interview and in English at the end.
"My greetings to the people of America, who are very dear and near to the hearts of the Iranian people," he said in Persian before answering the first question.
"I bring peace and friendship from Iranians to Americans," he said in English at the end.