WASHINGTON » Breaking a third-of-a-century diplomatic freeze, President Barack Obama and new Iranian President Hassan Rouhani spoke by telephone Friday and, in a historic shift from years of unwavering animosity, agreed to work toward resolving their deep dispute over Tehran’s nuclear efforts.

Rouhani, who earlier in the day called the United States a "great" nation, reached out to arrange the 15-minute call. 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.

Rouhani, at a news conference in New York, 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.

The new Iranian president has repeatedly stressed that he has "full authority" in his outreach to the U.S., a reference to the apparent backing by Iran’s ultimate decision-maker, Supreme Leader Ayatollah Ali Khamenei. Such support would give Rouhani a political mandate that could extend beyond the nuclear issue to possible broader efforts at ending the long estrangement between Tehran and Washington — and the West in general.

It remains unclear, however, 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.

"Friday’s telephone call — Obama at his desk in the Oval Office, Rouhani in a limousine on the way to the airport after diplomatic meetings at the United Nations — marked one of the most hopeful steps toward reconciliation in decades. The White House said an encouraging meeting between Secretary of State John Kerry and Iranian Foreign Minister Mohammad Javad Zarif this week was a crucial factor in the thaw. 

"This is part of a pattern that has led to a real breakthrough," said Iran scholar Gary Sick at Columbia University. "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. This is breathtaking." 

Obama came out to the White House briefing room to announce the conversation about an hour after the call ended. 

"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."

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.

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. 

"In phone convo, President #Rouhani and President @BarackObama expressed their mutual political #will to rapidly solve the #nuclear issue," another tweet said. 

The White House said that the tweets were an accurate description of the call, and that the Americans had been following the Twitter account recently to monitor Rouhani’s use of social media. A picture sent out by the account showed a broadly smiling Rouhani aboard his plane about to depart for Tehran "after historic phone conversation with @BarackObama."

Iran’s official news agency said the two "underlined the need for a political will for expediting resolution of West’s standoff with Iran over the latter’s nuclear program." The White House said the United States wants to move "expeditiously" with Iranian negotiations but isn’t setting a hard deadline. 

Rouhani has repeatedly stressed that he has "full authority" in his outreach to the U.S., a reference to the apparent backing by Iran’s ultimate decision-maker: Supreme Leader Ayatollah Ali Khamenei. Such support would give Rouhani a political mandate that could extend beyond the nuclear issue to possible broader efforts at ending the more than long diplomatic estrangement between Washington and Tehran. It remains unclear, however, whether obstacles will be raised by Iran’s hard-line forces such as the  Revolutionary Guard, which had warned Rouhani about moving too fast with his overtures with the West.

Mahmoud Ahmadinejad, Rouhani’s predecessor, had trouble with the supreme leader when Ahmadinejad attempted to challenge his power. The backlash weakened Ahmadinejad’s government and left him with less political power.

Rouhani was elected in June and took office Aug. 4 after campaigning on a promise to seek relief from U.S. and Western sanctions that have slashed Iran’s oil exports by more than half in the past two years, caused inflation to spike and undercut the value of the nation’s currency.

At issue most directly at present are suspicions outlined in reports from the U.N.’s International Atomic Energy Agency that Iran has worked secretly on trying to develop nuclear weapons. Tehran says it isn’t interested in atomic arms and only wants to develop nuclear technology for peaceful use.

The White House had reached out to Tehran earlier this month to offer a meeting on the sidelines of the United Nations General Assembly on Monday or Tuesday, but Rouhani declined at the time. But the U.S. and five negotiating partners emerged from a meeting with Iran Thursday declaring that a "window of opportunity has opened" to peacefully settle the nuclear standoff.

The White House said Iranian officials reached out Friday and indicated Rouhani would like to speak to Obama before leaving New York, and Obama’s aides quickly arranged the call.

Rouhani told reporters at the U.N., "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."

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 that Iranian nuclear weapon capability is 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.

Lara Jakes reported from the United Nations.