Barack Obama, the US president, has said he has spoken by phone with his Iranian counterpart Hassan Rouhani, making the call the first conversation between any US and Iranian presidents since 1979.
Obama, speaking from the White House, said after speaking with Rouhani that he believed the two countries could reach a comprehensive solution over Iran's nuclear programme.
The president said he and Rouhani had both directed their teams to work quickly to pursue an agreement.
He said the US will co-ordinate closely with its allies, including Israel, which considers an Iranian nuclear weapon capability to be an existential threat.
Obama said the conversation showed the possibility of moving forward and that it was a unique opportunity to make progress with Iran over an issue that has isolated it from the West.
Iranian and UN officials have been meeting to continue talks on how to investigate suspicions that Iran has worked secretly on trying to develop nuclear weapons, claims which are denied by Tehran.
Foreign language exchange
The impetus for the call came from Iranian officials, who US officials said told them hours earlier in New York that Rouhani wanted to speak to Obama before leaving the United Nations General Assembly.
The White House had indicated to Tehran earlier this week that it was open to an informal encounter between the leaders at the UN.
But the Iranians at the time said such a meeting was too complicated, raising questions as to whether Rouhani was wary of angering hardliners in Iran's clerical hierarchy.
The leaders' momentous conversation took place when Rouhani was on his way to the airport in his official limousine, the Iranian side said.
Obama spoke in English and Rouhani spoke Farsi as they chatted through interpreters, according to US officials.
But before hanging up, in an exchange that would have been thought impossible only days ago, Obama bade Rouhani "khodahafez" - farsi for "goodbye."
Rouhani replied "have a good day, Mr president" in English, according to tweets by the Iranian leader's office and a US official.