WASHINGTON — As he conducts a high-profile good-will visit to New York this week, Iran’s new president, Hassan Rouhani, says he is bringing a simple message of peace and friendship. But on Wednesday, Mr. Rouhani set off a political storm here and in Iran, with an acknowledgment and condemnation of the Holocaust that landed him in precisely the kind of tangled dispute he had hoped to avoid.

Mr. Rouhani, in an interview on Tuesday with CNN, described the Holocaust as a “crime that the Nazis committed towards the Jews” and called it “reprehensible and condemnable.” It was a groundbreaking statement, given that his predecessor, Mahmoud Ahmadinejad, denied the systematic extermination of Jews during World War II. Mr. Rouhani largely repeated his comments in a meeting with news media executives on Wednesday.

But a semiofficial Iranian news agency accused CNN of fabricating portions of Mr. Rouhani’s interview, saying he had not used the word Holocaust or characterized the Nazi mass murder as “reprehensible.” Mr. Rouhani spoke in Persian; officials at CNN said they used an interpreter provided by the Iranian government for the interview, which was conducted by Christiane Amanpour.

The dispute over his comments reflects the extreme delicacy of the Holocaust as an issue in Iranian-American relations. More broadly, it speaks to the political tightrope Mr. Rouhani is walking, trying to negotiate a nuclear deal with the United States that will ease sanctions to please everyday Iranians, without provoking a backlash by hard-liners.