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By Roberta Rampton WASHINGTON (Reuters) - President Barack Obama has told Iran's President Hassan Rouhani in an exchange of letters that the United States is ready to resolve its nuclear dispute with Iran in a way that allows Tehran to show it is not trying to build weapons, the White House said on Wednesday. "In his letter the president indicated that the U.S. is ready to resolve the nuclear issue in a way that allows Iran to demonstrate that its nuclear program is for exclusively peaceful purposes," said White House spokesman Jay Carney. "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. The White House comments are another sign of a potential thaw between the West and Iran on nuclear issues. The United States and its allies have imposed sanctions aimed at stopping Iran from seeking a nuclear weapons capability, but Iran has long insisted its program is for civilian purposes. Since Rouhani was elected as president in June, he has called for "constructive interaction" with the world. The head of Iran's nuclear energy organization said on Wednesday he saw "openings" on the nuclear issue. Obama said on Tuesday that he is willing to test the willingness of Rouhani to discuss the nuclear issue. "There is an opportunity here for diplomacy," Obama told Spanish-language network Telemundo in an interview. "And I hope the Iranians take advantage of it." Both Obama and Rouhani plan to be in New York next week for the U.N. General Assembly, but the leaders do not currently have plans to meet, Carney said. (Reporting by Roberta Rampton and Mark Felsenthal; editing by Christopher Wilson and Jackie Frank)