UNITED NATIONS — Descending on New York this week in a Shiite cleric’s traditional fine wool robes, Iran’s president, Hassan Rouhani, turned himself into a high-speed salesman offering a flurry of speeches, tweets, televised interviews and carefully curated private meetings.

On Tuesday, he capped his speech to the United Nations General Assembly with a nod to the Torah and the Psalms, which elicited applause and then, from him, the slightest hint of a smile. That day he also hosted a clutch of media executives as his chief of staff did what previously would have been unthinkable, meeting with a dozen influential American business leaders.

Over salmon kebabs in his hotel on Wednesday evening, he bluntly told a gathering of former United States diplomats and Iran scholars that he would never give up his country’s right to enrich uranium, but would swiftly resolve its nuclear standoff with the West. The next day he took aim at Israel’s nuclear arsenal in a public speech in the morning, and at night wooed his country’s influential, often skeptical diaspora with a banquet for 800.

But amid the fervent diplomatic theater, intended to end Iran’s isolation, it was at times difficult to tell whether Mr. Rouhani was a genuinely transformative Iranian leader, as his cabinet insisted, or a more polished avatar of the past, as his critics claimed.