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White House officials said Obama’s letter to Rouhani touched on the long-stalled negotiations over Tehran’s nuclear program, one of the main roadblocks to diplomacy between the two countries. Officials said Obama indicated that Washington was ready to resolve the nuclear issue in a way that would allow Iran to demonstrate that its program was exclusively for peaceful purposes.

“The letter also conveyed the need to act with a sense of urgency to address this issue because, as we have long said, the window of opportunity for resolving this diplomatically is open, but it will not remain open indefinitely,” Carney said.

Rouhani, in his first interview with a Western media outlet, told NBC News that he thanked Obama for his outreach and “expressed Iran’s viewpoint on the issues raised in his letter and some other issues.”

In 2009, shortly after taking office, Obama also wrote to Khamenei expressing a desire for a different type of relationship between their countries. People familiar with the outreach say Khamenei responded with a letter of his own but gave little ground and, ultimately, the communications fizzled.

Einhorn also predicted that negotiators from the U.S. and Iran will sit down for direct one-on-one talks about the nuclear issue in the near future — a direct negotiation that he said has not happened since 2009.

Any direct exchange between Obama and Rouhani at the United Nations would be largely symbolic, with substantive negotiations on Iran’s nuclear program almost certainly reserved for talks with officials from both governments.

Trita Parsi, the president of the National Iranian American Council, said Rouhani has a narrow window of opportunity to show the U.S. and the international community that he’s more serious about negotiations than his predecessors.

“He doesn’t have much time to show that his approach is more effective than the regime previously,” Parsi said. “It’s important for him to present something at the U.N. that is very memorable, that really adds to what he has already been doing over the last couple of weeks.”