“We don’t want further tension. Both nations need 2 think more abt future & try 2 sit down & find solutions to past issues & rectify things,” he, or somebody writing in his name, said on June 17. On the nuclear program, he commented: “Our program is transparent, but we can take more steps to make it clear to world that our nuclear program is within intl regulations.”

This seemingly reasonable outlook — refreshing after the ugly, confrontational approach of his predecessor, Mahmoud Ahmadinejad — has been reinforced by other recent moves. The most significant is Mr. Rouhani’s appointment of Mohammad Javad Zarif as foreign minister. In addition to being educated in the United States and serving many years as Iran’s ambassador at the United Nations, Mr. Zarif has been at the center of several rounds of secret negotiations over the years to try to overcome decades of enmity between the two countries.

Mr. Zarif is also being considered to lead a new round of nuclear negotiations with the major powers, replacing the conservative Saeed Jalili, who made things worse when he was in that job. At his first news conference, President Rouhani parried questions about possible direct talks with Washington — which will be essential at some point for any deal to be concluded — but said he was ready to “seriously engage and interact with other parties.”

It would be naïve to assume that the path to ending Iran’s isolation is now clear. Hostilities between America and Iran have hardened since the 1979 Islamic revolution. For some time after the covert nuclear program was discovered in 2002, Iranian officials shrewdly played a weak hand to divide the international community and avoid sanctions. It seems likely that Mr. Rouhani, with his benign demeanor, seductive tone and more “moderate” message, will be more focused, serious and skillful in negotiations than Mr. Ahmadinejad, but still unyielding in Iran’s core demand to retain significant nuclear capability.

Even so, there are strong forces propelling both sides toward a deal.

Harsh sanctions imposed by the United States, Europe and the United Nations since 2009 have devastated Iran’s economy, which Mr. Rouhani is desperate to revive. Although there is no evidence that Iran has produced a nuclear weapon, its program has steadily advanced, prompting both President Obama and Prime Minister Benjamin Netanyahu of Israel to warn of possible military action. At a time when the Middle East and South Asia are in turmoil, there are also many regional issues that could benefit from American-Iranian cooperation, including Afghanistan and Syria.

President Rouhani is sending strong signals that he will dispatch a pragmatic, experienced team to the table when negotiations resume, possibly next month. That’s when we should begin to see answers to key questions: How much time and creative thinking are he and President Obama willing to invest in a negotiated solution, the only rational outcome? How much political risk are they willing to take, which for Mr. Obama must include managing the enmity that Israel and many members of Congress feel toward Iran?

And finally: Do the two sides have the courage to resolve a conflict that has been decades in the making?