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, 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.

In television interviews and public addresses throughout the week, he repeatedly sought to cast himself as a moderate ready to do business with the West. But it was also clear that whatever he said here was closely, instantly dissected at home, raising uncertainty over whether he could truly deliver a compromise with the West, if that is what he sought.

And so he condemned the Nazis in a TV interview, but quickly hedged by saying he was not a historian. And even as he called for “time bound” talks to resolve the nuclear standoff, he skipped a lunch at which he might have had the chance to meet President Obama and shake his hand. Even charmed diplomats pointed out that he offered no concrete proposals, while also noting that he had received nothing concrete from Western officials to take back to his constituents at home.

Those who watched him closest this week describe Mr. Rouhani as serious, controlled and single-mindedly focused on message. He seemed intent to convey that he was prepared to take concrete steps to normalize relations with the West, that he was reasonable and that he enjoyed the backing of the street and his country’s religious establishment. He also seemed to be in somewhat of a rush, even while saying events might have been moving too fast.

“He did not come to New York to negotiate with speeches or throw in the towel and surrender. He came to New York to start negotiations,” said Vali Nasr, dean of the School of Advanced International Studies at Johns Hopkins University. “He is very clever, very pragmatic, but he’s also now showing himself to be bold, a risk-taker. He is taking the biggest risk any Iranian has in reaching out to the West.”

The contrast with his predecessor, Mahmoud Ahmadinejad, could not be more stark. Mr. Ahmadinejad used his podium at the General Assembly to blast Israel, deny the Holocaust and dangle the notion that Sept. 11 was the handiwork of Americans. Mr. Rouhani, in his public speeches, has mentioned Israel only once, calling on it to sign the Nonproliferation Treaty.

All the same, he has insisted on Iran’s right to build what he insists is a civilian nuclear program. At a dinner for about 20 former diplomats and Iran scholars Tuesday night at the One U.N. New York, a hotel across the street from the United Nations building, one dinner guest recalled that Mr. Rouhani was bluntly asked: What is Iran doing and why is it doing it?

“His answer was very simple,” said the dinner guest, who could not be named because it was a confidential meeting. “We are enriching. We are doing it because it is our right.”

The only time the usually unflappable Mr. Rouhani was mildly exercised, the first dinner guest said, was when he spoke of Israel’s complaints about Iran’s nuclear program. Mr. Rouhani, he recalled, sharply pointed out that Israel itself had nuclear weapons.

The next morning, speaking at a meeting on disarmament, Mr. Rouhani called on Israel to give up its nuclear weapons.

Remarks like that prompted some critics to say that Mr. Rouhani was simply a camouflaged version of Mr. Ahmadinejad, pressing the same aims. “Rouhani came here today to cheat the world, and unfortunately many people were willing to be cheated,” Israel’s minister of intelligence and internal affairs, Yuval Steinitz, said at a news conference Tuesday at the United Nations.

“The main thing for me is that the substance is very similar to Ahmadinejad’s, but he says it in a much kinder and gentler way,” said Gary Samore, a former Obama adviser, and now the president of United Against Nuclear Iran. “That’s the definition of a charm offensive.”