Hassan Rouhani wrote to the American president, US officials confirmed, as well as to the leaders of the five other powers heading efforts to resolve the 12-year standoff over Iran's nuclear programme.
The content of the letters was not known. But Rouhani, whose 2013 election led to the current diplomatic push, also phoned the leaders of Russia, China, Britain and France, his office said.
"We are acting in the national and international interest and we should not lose this exceptional opportunity," Hassan Rouhani told British Prime Minister David Cameron by phone, the presidency said.
Francois Hollande, "insisting on Iran's legitimate right to use peaceful nuclear power, insisted on the need to work towards a lasting, robust and verifiable agreement," the French presidency said.
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Highlighting the difficulties of talks that resumed in Switzerland Thursday between US Secretary of State John Kerry and his Iranian counterpart, Rouhani also said Iran wants all sanctions lifted.
"The peaceful character of (Iran's) nuclear activities and the necessity to annul all the unjust sanctions can lead us to a final deal," Rouhani's office quoted him as telling Cameron.
Cameron "emphasised the importance of Iran showing flexibility on the outstanding issues in order for a deal to be reached," Downing Street said afterwards.
Kerry's talks in Lausanne with Foreign Minister Mohammad Javad Zarif and officials from the powers are aimed at agreeing the outlines of a nuclear deal by March 31 after two missed deadlines in 2014.