WASHINGTON — The Iranian president, his visit to the U.S. nearing its end, makes contact with the White House. As his car inches through New York’s snarled traffic, he hears Barack Obama’s voice on the phone as the U.S. president sits at his desk in the Oval Office.

Fifteen minutes later, the two men say goodbye in each other’s language.

And with that, a generation-long rift between the U.S. and Iran is closer to being bridged.

Iranians awoke Saturday to learn that their president, Hassan Rouhani, had spoken directly to Obama, breaking through a barrier that had left American and Iranian presidents divorced from such contact for 34 years. The two presidents pledged to resolve concerns about Iran’s nuclear ambitions, which have isolated Iranians from the global community and led to crippling economic sanctions.

The appetite for serious talks having been tested at a presidential level, the focus turns to negotiations among foreign ministers and other officials from the five permanent members of the U.N. Security Council plus Germany, who together will chart a path forward, a senior Obama administration official said. The group wants Iran to present a more detailed proposal before or at the next round of talks, scheduled in Geneva on Oct. 15-16.

Rouhani’s aides initially reached out to arrange the call, said officials, who weren’t authorized to comment by name and demanded anonymity. But it was Obama who signaled days earlier he was willing to meet with his Iranian counterpart.

By the end of the call, Obama was suggesting that a breakthrough on the nuclear issue could portend even deeper ties between the U.S. and Iran, a notion that would have seemed unfathomable in recent years, when Rouhani’s predecessor was describing America in satanic terms.

The shift in tone aside, there was immediate skepticism that Iran was cynically seeking to procure relief from economic sanctions but would not take concrete action to assuage global concerns that it is seeking to build nuclear weapons.

The U.S. and Western allies imposed the sanctions after years of stonewalling inspections and secrecy about its activities fueled fears about its intentions — especially as they relate to Israel, a staunch U.S. ally and the target of much of Iran’s most fiery rhetoric. Iran insists its nuclear program is strictly for peaceful purposes.

Obama said that the U.S. will coordinate closely with its allies — including Israel, which considers a nuclear-armed Iran to be an existential threat.