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 U.S. 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 U.S. 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 U.S. 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 U.S. and Iran as “great nations.” The night before, U.S. 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.

The U.S. and Western allies imposed the penalties after years of Iran’s stonewalling inspections and secrecy about its activities fueled fears about its intentions — especially as they relate to Israel. Iran insists its nuclear program is strictly for peaceful purposes.

House Majority Leader Eric Cantor, R-Va., criticized Obama for failing to pressure Rouhani on Iran’s support for Islamic extremist groups and on human rights issues.

He said the U.S. is fooling itself if it thinks that Rouhani, who took office in August after running on a more moderate platform, isn’t beholden to Iran’s supreme leader, Ayatollah Ali Khamenei, who controls matters of state, including the nuclear program.

For Obama, the call marked a realization of sorts of a stance he took in 2008, when he was first running for president and saying he would be willing to meet with leaders from nations such as Iran, Syria and North Korea without conditions. The policy earned him rebukes from critics who questioned what they derided as a Pollyanna approach to security threats.

The offer on the negotiating table for Rouhani would give Iran some relief from the economic penalties and pledge not to impose new ones. In exchange, Iran would end uranium enrichment that nears or reaches 20 percent, a level just a few steps from what’s needed to produce fuel for an atomic weapon.

The deal, offered last February, would require suspended enrichment at Iran’s fortified underground Fordo facility and increased access for U.N. inspectors.

“It’s way too soon to presume either the prospect of an agreement on the nuclear program, which we hope to be able to achieve, but we’re quite sober about the potential for that,” Obama’s national security adviser, Susan Rice, told CNN’s “Fareed Zakaria GPS.”

She added that “if we could have a peaceful resolution of the nuclear program and an end to Iran’s support for terrorism and other behavior that has concerned us over many years, then we could begin a serious discussion about the future.”

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.

Obama is set to meet with Israeli Prime Minister Benjamin Netanyahu at the White House on Monday.

(AP)