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Mr. Netanyahu, rattled by Mr. Obama’s desire to engage Iran, has warned that Mr. Rouhani, with his professorial demeanor and moderate tone, is a wolf in sheep’s clothing. Yet Iran’s hard-liners, Mr. Sadjadpour said, “probably view him as sheep in wolf’s clothing.”

The complex political crosscurrents were on display in the Iranian news media’s coverage of Mr. Rouhani’s day at the United Nations. A reformist newspaper, Shargh, published pictures of Mr. Rouhani and Mr. Obama during their speeches, with the headline “Perhaps Another Time” — a reflection of the letdown among average Iranians about the missed opportunity for a handshake.

But another paper, Kayhan, which is close to the supreme leader, Ayatollah Ali Khamenei, expressed horror over the possibility that “the clean hand of our president would for moments be in the bloody clench” of Mr. Obama.

Advisers and analysts close to the government in Tehran said that after weeks of conciliatory statements and gestures by Mr. Rouhani, the excitement had gotten out of hand.

“We need to gain something from the Americans, before we pose and smile with them,” said Hamid-Reza Taraghi, an official who is one of the few trusted to interpret the speeches of Ayatollah Khamenei. “Of course, Mr. Rouhani also needed to convince some at home that he is not making any wild moves.”

Mr. Rouhani himself suggested that a meeting would have been premature and might actually have jeopardized the longer-term goal of striking an agreement on the nuclear program. Speaking to editors and columnists in New York on Wednesday, he said, “I believe we did not have enough time to make it happen.”

“If we do not take our first steps carefully,” he said, “we may not at the very least be able to obtain mutual goals that are in our minds.”

White House officials, though deflated, said Mr. Rouhani’s decision showed he is an astute political player who knows how to calm hard-liners at home while charming audiences abroad. Those are skills they say he will need to navigate the treacherous waters of Iranian politics.

“The issue of the relationship between the United States and Iran is incredibly controversial within Iran,” said a senior administration official. “For them it was just too difficult to move forward with that type of encounter at the presidential level, at this juncture.”