In Iran, many had been disappointed when Mr. Rouhani failed to show up Tuesday at a United Nations luncheon, where he had been expected to shake hands with Mr. Obama. But the Friday call as Mr. Rouhani was heading to the airport to fly home to Iran, after four days of frenetic diplomacy in the United States, was almost as good as a handshake.

“This voice contact has for now replaced the actual shaking of hands, but this is clearly the start of a process that could in the future lead to a face-to-face meeting between both leaders,” said Amir Mohebbian, a political adviser close to Iran’s supreme leader, Ayatollah Ali Khamenei.

“After the positive meeting between the foreign ministers of Iran and the United States on Thursday, we could see this coming,” Mr. Mohebbian said in an interview, referring to Foreign Minister Mohammad Javad Zarif and Secretary of State John Kerry. “This was a polite farewell, a thank you for all the positivity from Iran.”

If talks on Iran’s nuclear program next month go well, he said, “we could witness a meeting after that.”