The phone call may signal the beginning of the resolution of the Iran nuclear weapons crisis and help the Islamic nation escape the clutches of economic sanctions.
The Guardian quoted Obama as saying in his White House statement, "While there will be significant obstacles and success is by no means guaranteed, I believe we can reach a comprehensive solution. I do believe that there is a basis for a resolution."
The conversation was held with the help of interpreters, said sources in the Obama administration, adding that the US President "conveyed his deep respect for the Iranian people to Rouhani".
The Iranian President, considered a moderate leader by many, urged Obama to “have a nice day” before ending the conversation.
The US President responded with Khodahafez, which means good bye in Persian and translated literally, stands for ‘May God go with you’.
Earlier in the day, Rouhani called the United States a "great" nation in a sharp reversal from his predecessors and expressed hope that at the very least, the two governments can stop the escalation of tensions.
Wrapping up his first trip to the United States as Iran's new leader, Rouhani said President Obama struck a new tone in his address to the United Nations General Assembly this week, which he welcomed.
He said he believes the first step to a meeting between the two leaders was taken Thursday at a meeting on Iran's nuclear programme, where the foreign ministers of both nations talked for the first time in six years.
"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 told a press conference at a hotel near UN headquarters.
He expressed hope that "the views of our people, the understanding of each other, will grow, and at the level of the two governments that at the very least we can as a first step stop further escalation of tensions and then reduce tension as a next step and then pave the way for achieving of mutual interests."
The new Iranian President's demeanour is in sharp contrast to his predecessors, most of whom had branded America as the 'Great Satan', and whose supporters had often taken to the streets to chant ‘Death to America’.
Sources in the White House indicated that the Iran President and his entourage pitched the idea for the phone call after considering, and ruling out, a meeting with the US President.
A meeting between the leaders of the two hostile nations, though a great photo-opportunity for journalists, would be 'too complicated', said the Guardian.
The daily quoted Obama telling White House correspondents later, “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”.
Image: US President Barack Obama talks with Iranian President Hassan Rouhani during a phone call in the Oval Office at the White House in Washington ' Photograph: Pete Souza/Reuters
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