Ban, at a news conference, was asked about Iranian President Mahmoud Ahmadinejad, who since coming to power in August last year has caused an outcry by terming the Holocaust a ''myth'' and calling Israel a ''tumor'' in the West Asia.
Ahmadinejad just ended a two-day international conference on the Holocaust that was dominated by speakers who questioned the extermination of 6 million Jews by the Nazis in World War Two.
''Denying historical facts especially on such an important subject as the Holocaust is just not acceptable,'' Ban said.
''Nor is it acceptable to call for the elimination of states or people,'' Ban said. ''I would like to see this fundamental principle respected in both rhetoric and practice by all the members of the international community.'' A former South Korean foreign minister, Ban spoke to reporters after he took an oath of office in the UN General Assembly as secretary-general to succeed Kofi Annan. He assumes his post on January. 1.
Ban left open the possibility of visiting Tehran on a series of issues.
''Whenever and when the situation requires me to do, I am prepared to engage in dialogue with the Iranian people,'' he said.
But he avoided commenting on questions about Iran's nuclear ambitions, now the subject of a resolution before the UN Security Council.