"I would like to say to American people: I bring peace and friendship from Iranians to Americans," he said.

Rouhani is in many ways the "it" man of this U.N. General Assembly, where Western leaders are trying to gauge whether his diplomatic overtures will translate into concrete policy changes.

He has recently exchanged letters with U.S. President Barack Obama, and there had been suspicion brewing in diplomatic circles that the two leaders would meet face-to-face, informally, at the United Nations in New York.

"There were some talks about it," Rouhani told Amanpour through a translator. "And preparation for the work was done a bit as well."

"The United States declared its interest in having such a meeting, and in principle Iran could have under certain circumstances allowed for it to happen," he said. "But I believe we didn't have sufficient time to really coordinate the meeting to the full extent that we needed to."

Two senior U.S. administration officials told CNN on Tuesday that the encounter was called off because it was considered "too complicated" for Iran back home.

Complicated domestic politics or not, the Iranian president made clear that he has full permission from Iran's supreme leader, Ayatollah Ali Khamenei, to negotiate with the West.

"I think that the president of Iran has the authority whenever the national interest of the country is involved," Rouhani told Amanpour. "The supreme leader of Iran has said that should negotiations be necessary for the national interest of the country, he is in fact not opposed to it."

"Now, if an opportunity was created today, had arisen today," the Iranian president said, "and the prep work for that had been done, most probably the talks would have haven taken place, primarily focused on the nuclear issue or the developments on the Middle East. Therefore the supreme leader, I can tell you, has given permission for my government to freely negotiate on these issues."

Rouhani stands in stark contrast to his predecessor, Mahmoud Ahmadinejad, who used his speeches at the U.N. to spew rhetoric; he was famous for his questioning of the Holocaust.

"I have said before that I am not a historian, and that when it comes to speaking of the dimensions of the Holocaust it is the historians that should reflect on it," Rouhani told Amanpour. "But in general I can tell you that any crime that happens in history against humanity, including the crime the Nazis committed towards the Jews, as well as non-Jewish people, was reprehensible and condemnable as far as we are concerned."