The last direct conversation between the leaders of the two countries was in 1979 before the Iranian Revolution toppled the pro-U.S. shah and brought Islamic militants to power. Obama said the long break "underscores the deep mistrust between our countries, but it also indicates the prospect of moving beyond that difficult history."
"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 at the White House. Iran's nuclear program has been a major concern not only to the United States but to other Middle Eastern nations especially Israel and to the world at large.
Earlier, at a news conference in New York, Rouhani linked the U.S. and Iran as "great nations," a remarkable reversal from the anti-American rhetoric of his predecessors, and he expressed hope that at the very least the two governments could stop the escalation of tensions.
"I want it to be the case that this trip will be a first step, and a beginning for better and constructive relations with countries of the world as well as a first step for a better relationship between the two great nations of Iran and the United States of America," Rouhani said at the end of his four-day debut on the world stage to attend the annual U.N. General Assembly.
Iran scholar Gary Sick at Columbia University described the events as "breathtaking" and said the weeks of slow warming led to Friday's dramatic step.
"This is part of a pattern that has led to a real breakthrough," Sick said. "And basically what's happening is that the ice that has covered the U.S.-Iran relationship for over the last 30 years is starting to break. And when ice starts to break up, it goes faster than you think."
The groundwork for the detente was set years ago.
During his 2008 presidential campaign, Obama repeatedly said he would be willing to negotiate with Iran to ease tensions and move toward a nuclear settlement. That fell by the wayside, however, when Mahmoud Ahmadinejad was re-elected president in 2009 in a disputed vote that spurred the worst domestic unrest since the 1979 Iranian Revolution and, in turn, a violent crackdown on the political opposition.
The nuclear talks between Iran and world powers have stagnated since then, prompting a series of blistering economic sanctions on the Islamic Republic that have slashed oil exports, made it difficult to conduct international bank transfers, drastically driven up inflation and devalued the currency. Rouhani took office Aug. 4 after overwhelmingly defeating several conservative candidates in the first round of elections on a promise to seek relief from the sanctions and has said he has "full authority" from Supreme Leader Ayatollah Ali Khamenei to do so.
Khamenei may be mindful that the pressure of sanctions could fuel a wave of unrest like the one in 2009, and experts believe this is one reason he appears to have given his blessing to Rouhani to pursue negotiations.
Rouhani is no stranger to the nuclear talks. In 2003, he was on the Iranian team that negotiated a settlement with European nations under which it agreed to an additional safeguards protocol, suspend enrichment and allow additional inspections by the International Atomic Energy Agency. The deal fell through when Iran reneged on its pledge to allow inspectors unfettered access to the nuclear sites, and then it withdrew from the protocol.
The offer currently on the negotiating table would give Iran some sanctions relief and pledge not to impose new penalties in exchange for ending uranium enrichment that nears or reaches 20 percent, a level that is just a few steps from what is needed to produce fuel for an atomic weapon.
The deal, which was offered last February, would also require Tehran to suspend enrichment at its fortified underground Fordo facility and prevent it from being able to re-start that process quickly and it would have to grant U.N. inspectors greater access to monitor the nuclear program.
Iran maintains any agreement also acknowledge its right under an international treaty to enrichment uranium, a condition Rouhani repeated in his speech to the General Assembly. He also said all nations not just Iran should declare their nuclear programs as solely peaceful.
Iranian Foreign Minister Mohammad Javad Zarif met Thursday with the five permanent members of the U.N. Security Council the U.S., Russia, China, Britain and France and Germany. He gave an "energetic" and "thoughtful" 15- to 20-minute presentation that outlined Iran's interests, its desire to reach and implement an agreement within a year and some general ideas on how that could happen, according to a senior U.S. official present.
Zarif's comments were well received, but each member of the group noted that the words have to be followed by actions and expressed a desire for the Iranians to flesh out their ideas, which appeared to be based on the February offer, according to the official. The official spoke on condition of anonymity to discuss the closed-door discussions.
The group of nations wants Iran to present a more detailed proposal before or at the next round of negotiations that are scheduled in Geneva on Oct. 15-16, the official said.
The White House said Obama told Rouhani he wants to see the return of two Americans detained in Iran former U.S. Marine Amir Hekmati and Christian pastor Saeed Abedini as well as retired FBI agent Robert Levinson, who went missing in Iran in 2007.
Obama came to the White House briefing room to announce the conversation about an hour after the call ended. The White House said it doesn't know what made Rouhani initiate the call, but that it sees an encouraging meeting between Secretary of State John Kerry and Zarif this week as a crucial factor.
The White House had reached out to Tehran earlier this month to offer a meeting on the sidelines of the U.N. General Assembly on Monday or Tuesday, but Rouhani declined at the time. Rouhani may have asked for the phone call before he left the U.S. to avoid the impression that he snubbed Obama at the United Nations when the two failed to meet.
"I do believe that there is a basis for resolution," Obama said. He said an agreement could usher in a new era of mutual interest and respect between the United States and Iran, but he also said it would require Iran to take "meaningful, transparent and verifiable actions" concerning its nuclear program.
"A path to a meaningful agreement will be difficult. And at this point both sides have significant concerns that will have to be overcome," Obama said. "But I believe we've got a responsibility to pursue diplomacy and that we have a unique opportunity to make progress with the new leadership in Tehran."
In a sign of modernization in Iran, the news broke on Twitter a couple of minutes before Obama spoke, in an account that people close to Rouhani say is written by a former campaign aide who remains in close contact with the president's inner circle. A Rouhani adviser said the president doesn't tweet himself or direct what is written. The White House said that the tweets were an accurate description of the call.
The two men talked through interpreters, but the tweet from @HassanRouhani said they ended by signing off in each other's language. "In a phone conversation b/w #Iranian & #US Presidents just now: @HassanRouhani: 'Have a Nice Day!' @BarackObama: 'Thank you. Khodahafez,'" the tweet said, quoting Obama as using the Farsi word for good-bye.
It remains unclear whether obstacles will be raised by Iran's hard-line forces such the powerful Revolutionary Guard, which had warned Rouhani about moving too fast with his overtures with the West. Even so, Iran's official news agency said Obama and Rouhani "underlined the need for a political will for expediting resolution of West's standoff with Iran over the latter's nuclear program."
Despite the animosity between the two countries, U.S. officials have been in contact with Iranians numerous times over the last three decades, including President Ronald Reagan secretly sending his national security adviser, Robert McFarlane, to Iran as part of an arms-for-hostages deal. And the two countries have had episodes of cooperation, particularly in the first Gulf war. The coldest relations were in the first phase after the 1979 Revolution and the taking of American hostages after the U.S. Embassy was overrun and during the Ahmadinejad era.
Both sides said the presidents directed their top diplomats, Zarif and Kerry, to continuing pursing an agreement, with Iranian and U.N. officials have agreed to meet again Oct. 28. Obama said the U.S. will coordinate closely with its allies including Israel, which considers Iranian nuclear weapon capability a deadly threat.
Israeli Prime Minister Benjamin Netanyahu's office has said his meeting on Monday with Obama at the White House will focus on the Iranian issue.
Israel has viewed Rouhani's outreach to the West with great skepticism, saying he is trying to trick the world into easing sanctions and hoping to buy time while he pushes forward with attempts to build a nuclear weapon. Israeli leaders have compared Rouhani's diplomacy to that of North Korea, which quietly developed a nuclear weapon while engaging the West.
The U.S. informed Israel of the call, a senior administration official said.
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Lara Jakes reported from the United Nations. Associated Press Matthew Lee contributed to this report from the United Nations.
On Twitter: Nedra Pickler at https://twitter.com/nedrapickler and Lara Jakes at https://twitter.com/larajakesAP