US President Barack Obama talks with Iranian President Hassan Rouhani during a phone call in the Oval Office at the White House in Washington September 27, 2013. US President Barack Obama and new Iranian President Hassan Rouhani held the historic phone call on Friday, in the highest level conversation between the estranged nations in more than three decades. [Photo/Agencies]

WASHINGTON — Iranian President Hassan Rouhani was ending his visit to the United States and inching through New York's notorious traffic when the call came from President Barack Obama in the Oval Office.

Fifteen minutes later, the two say goodbye in each other's language, and a generation-long rift between the US and Iran was that much closer to being bridged.

Iranians awoke Saturday to learn about the groundbreaking conversation, the first in more than three decades between leaders of the two countries.

They pledged to resolve concerns about Iran's nuclear ambitions, which have isolated Iranians from the rest of the world and led to crippling economic penalties.

Upon his arrival in Tehran on Saturday, Rouhani was met by both cheering supporters and opposition hardliners who tried to block his motorcade.

Several dozen protesters shouted "Death to America" and at least one reportedly hurled a shoe, a gesture of contempt. Supporters greeted Rouhani with cheers and placards praising his peace efforts.

The focus now turns to negotiations among foreign ministers and other officials from the five permanent members of the U.N. Security Council plus Germany. The group wants Iran to present a more detailed proposal before or at the next round of negotiations, scheduled in Geneva on Oct. 15-16, according to an Obama administration official.

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 US and Iran. Such a notion would have seemed unthinkable in recent years, when Rouhani's predecessor was describing America in satanic terms.

The telephone call capped a week of seismic shifts in the relationship while Rouhani was in the US for an annual U.N. meeting. Obama had left open the possibility of an exchange with Rouhani, but the Iranian later said the timing wasn't right.

But hours before the phone call, at a news conference in New York, Rouhani linked the US and Iran as "great nations." The night before, US and European diplomats were hailing a "very significant shift" in Iran's attitude and tone in the first talks on the nuclear standoff since April.

"While there will surely be important obstacles to moving forward, and success is by no means guaranteed, I believe we can reach a comprehensive solution," Obama told reporters Friday at the White House.