In a historic moment that could eventually redefine a generation of US-Iran enmity, President Barack Obama spoke to Iranian President Hassan Rouhani by phone today.

The 15-minute call capped a dramatic week at the United Nations General Assembly in which moribund nuclear talks with Iran were revitalized and frenetic diplomacy raised hopes of fresh and unprecedented progress.

"Just now I spoke on the phone with President Rouhani of the Islamic Republic of Iran," Mr. Obama said at a press conference this afternoon.

The call, which took place as the Iranian leader traveled to the airport, was the first direct contact between US and Iranian presidents since the 1979 Islamic revolution toppled the pro-West Shah.

The turbulent history of mutual antagonism includes a 444-day hostage saga of US diplomats in Tehran, decades of overt and covert conflict, and a standoff over Iran's controversial nuclear program that has at times risked war.

But Iran has waged a charm offensive since the mid-June election of the centrist cleric Rouhani, who declared that his victory for "moderation" would extend to reengagement with the West and improving Iran's sanctions-hit economy. Skeptics of Iran's intentions, such as Israel's Benjamin Netanyahu, have derided Rouhani as a "wolf in sheep's clothing."

Obama said today he saw a transformed political change that created "a new opportunity to make progress in Tehran." The president said he told Rouhani of "my deep respect for the Iranian people."

"Now, we’re mindful of all the challenges ahead. The very fact that this was the first communication between an American and Iranian president since 1979 underscores the deep mistrust between our countries, but it also indicates the prospect of moving beyond that difficult history. I do believe that there is a basis for resolution."

That sentiment was also expressed in Rouhani's semi-official Twitter account, where he described what Obama told him across three tweets strung together: "I express my respect for you and ppl of #Iran. I'm convinced that relations between Iran and US… will greatly affect region. If we can make progress on #nuclear file, other issues such as #Syria will certainly be positively affected… I wish you a safe and pleasant journey and apologize if you're experiencing the [horrendous] traffic in #NYC."

Rouhani described his response to Obama in four tweets: "In regards to #nuclear issue, with political #will, there is a way to rapidly solve the matter… We're hopeful about what we see from P5+1 and your [government] in particular in coming weeks and months… I express my gratitude for your #hospitality and your phone call. Have a good day Mr. President… Thank you, Khodahafez [God preserve you]."

A final tweet showed a smiling Rouhani on his airplane "after historic phone conversation with @BarackObama…about to depart for Tehran."

"The institutionalized enmity that has estranged the two governments – but never the two peoples – for more than 34 years will not be undone overnight," said Trita Parsi, president of the National Iranian American Council in a statement.

"Through the phone call, both leaders have shred the taboo of contact that protected this enmity and have unleashed forces of peace and moderation. While the final outcome of this courageous journey remains unknown, both sides have shown the courage and will to travel the diplomatic path towards its final destination."

Early indicators

Strong indications of a turning point began when Iran’s Foreign Minister Mohammad Javad Zarif met with counterparts of six world powers yesterday in a bid to change the dynamic after 17 months of fruitless talks.

That was followed by a historic one-on-one for 30 minutes with US Secretary of State John Kerry – the most substantial high-level US-Iran contact in decades.

In the first practical application of the change promised by Rouhani, who made his international debut this week, Mr. Zarif presented a number of new ideas and short timelines to limit Iran’s nuclear program so that it can never produce an atomic bomb. In exchange, he called for the lifting of US, European and UN sanctions that have crippled Iran’s economy.

“The Kerry-Zarif meeting is more important than any handshake between Rouhani and Barack Obama,” says Ali Vaez, the senior Iran analyst for the Brussels-based International Crisis Group, referring to expectations earlier in the week of a symbolic handshake at the UN General Assembly that did not happen because of the Iranian concerns about pushback at home.

But there is substantial history working against a rapprochement: The US and Iran have been archenemies in word and deed since Iran’s 1979 Islamic revolution toppled the US-backed Shah.

“This is a good start, but all sides should temper expectations,” says Mr. Vaez, speaking before the Obama-Rouhani phone call. “Like hurdling in track and field, springing over the first obstacle does not guarantee victory. But without it, the race is lost.”

Speaking today just hours before departing New York for Iran, Rouhani said he saw a "great deal of progress" in "reconstructing" Iran's global standing and that he hoped that his trip was a "first step" to more constructive relations between "two great nations" of Iran and the US.

"I believe our success was greater than our expectations," Rouhani said.

Mr. Kerry said Thursday night that he and ministers of the P5+1 group (the US, Russia, China, Britain, France and Germany) found Zarif’s presentation to be “very different in tone and very different in the vision…with respect to possibilities of the future.”

But even Zarif cautioned that so far the atmospheric change – significant as it is – was words only, with actions still to come. Deep-rooted skepticism underscores predictions of future progress, after a decade of grappling with Iran’s nuclear file, and setbacks amid a cacophony of biting rhetoric.

“We agreed to jumpstart the process so that we could move forward with a view to agreeing first on the parameters of the end game…and move toward finalizing it hopefully within a year’s time,” said Zarif. “I thought I was too ambitious, bordering on naivete. But I saw that some of my colleagues were even more ambitious and wanted to do it faster.”

Zarif said he was nevertheless "optimistic," but added, “Now we [all] have to match our words with actions. I hope that’s not too difficult."

No weapons, just energy

Iran has consistently rejected the construction of a bomb in public statements, citing religious prohibitions against all weapons of mass destruction. Rouhani, a centrist cleric whose shock first-round victory over conservative candidates in June – including Iran’s previous nuclear negotiator Saeed Jalili – said yesterday that “no nation should possess nuclear weapons,” and that any use of them would be a “crime against humanity.”

But past negotiations have foundered in part by the long-standing insistence of the US, some European nations, and Israel, that Iran halt all uranium enrichment, even production intended to create nuclear fuel for energy purposes. Purified to higher levels, the material can be used in nuclear weapons.

In the last decade, Iran has increased its number of centrifuges that purify uranium from 160 to more than 18,000. Recognizing that Iran has already achieved "industrial scale" enrichment, in Rouhani's words, most analysts expect the final deal to include enrichment on Iranian soil.

Rouhani, speaking Thursday night to Iran analysts and journalists gathered by the Asia Society and Council on Foreign Relations, said his government was “prepared to leave no stone unturned” to reassure the world that Iran’s purpose was to produce power.

But he also stated that Iran will “never forgo our inherent right to benefit from peaceful nuclear technology, including enrichment.”

The time to achieve something "tangible," such as some sanctions relief, is tight for Rouhani – just "three to four months, tops," says an Iranian diplomat who asked not to be named.

"The problem is there are hardliners in Iran who want to prove he's wrong" about seeking engagement with the West, he says.

Unusual in every way

The P5+1 talks yesterday were held in UN Security Council chambers and thrown together to include Zarif just days ago, so they proved more relaxed than the typical P5+1 meetings in Istanbul, Baghdad, Moscow and Almaty, Kazakhstan.

Ministers chatted amiably with the Iranians – an uncommon practice compared to previous sessions – and the decision where and when to hold the next round, which in the past had sometimes dragged on for weeks, was agreed to in a minute.

The next talks are slated for Geneva, from Oct. 15- 16.

After one-and-a-half years of negotiating with Mr. Jalili, the arch-conservative former head of Iran’s Supreme National Security Council who offered little flexibility and favored long monologues to hammer home a point, veterans of past rounds were floored by the difference.

“To have the Iranian minister open the talk was in itself a positive change in the dynamic. All ministers engaged with that,” said EU foreign policy chief Catherine Ashton, who chairs the talks on behalf of the P5+1. “The question is how far you can go in three months, or six months or 12 months [which] is a good timeframe to think about some serious implementation on the ground.”

A senior State Department official described Zarif’s presentation as “thoughtful” and said it broke new ground because Iran had never before spelled out its own vision of the endgame. He added that it could be fully implemented within a year.

“It was a very useful insight into Iranian interests, thinking, process, what their timeline is,” said the US official. “Is it enough granularity that you need to really know what you’re doing? Not yet. But for – certainly in the two years I’ve been doing this, no Iranian I’ve met with has sat down and said in such expansive terms, ‘Here’s what we’re willing to talk about.’”

The P5+1 ministers “welcome this opening… but the proof is in the pudding,” said the US official. “Virtually every minister talked about the need for concrete results and concrete measures that showed that there was – brought to life, in real terms, what Foreign Minister Zarif laid out to the ministers today.”

Ask and we'll deliver

The US official said that the one-on-one with Mr. Kerry began at the end of the P5+1 meeting, when Kerry leaned over to Zarif, who sat beside him, and asked, “Shall we talk for a few moments?” They went into an adjoining room for half-an-hour, in a meeting that the White House has since said laid the groundwork for the direct Obama-Rouhani phone call.

While the P5+1 meeting was underway, Rouhani spoke at a gathering of analysts and journalists. The US-educated Zarif arrived at the venue toward the end of the event and was invited to take the microphone to give the turbaned president – and the audience – a brief assessment of the talks, which he did.

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Rouhani was then questioned about his reaction: “You asked for the first step – they took it,” he said, smiling.

Zarif added, “This was a new beginning.”