“I think the U.S. president is clearly extending a hand to Iran and hoping to get a handshake back,” said Cirincione.

There was hope for a literal handshake earlier, at a U.N. luncheon, but U.S. officials said a meeting was offered but turned down by Iran. The Iranians said to hold even a brief meeting between the two presidents would be "too complicated."

Jessica Tuchman Mathews, of the Carnegie Endowment for International Peace, says such difficulties shouldn't be a surprise.

“Even if Rouhani has for now the supreme leader’s support, there are a lot of politicians in Iran that would like to see him fail, whose economic and political fortunes are made by no relation with the U.S.,” said Mathews.

Still, Iran has agreed to pursue confidence building measures. Iran analyst Geneive Abdo says it could be the first step in a long process.

“It’s imperative for the United States to convince the Iranians that they too want change and to end the hostility and that now the long process of doing that has begun,” said Abdo.

The next step may come when U.S. Secretary of State John Kerry meets with Iranian Foreign Minister Javad Zarif in the highest-level meeting between the two countries in decades.