"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.
Rouhani, whose 2013 election led to the biggest effort in years to end the decade-old standoff over Iran's nuclear activities, also spoke to Russian President Vladimir Putin and France's Francois Hollande.
"Hope was expressed for success at the new round of talks in Lausanne," the Kremlin said in a statement, while noting with "satisfaction the progress" made over previous weeks of talks.
But highlighting the difficulties of talks that resumed in Switzerland today 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.
The six powers negotiating with Iran -- the United States, China, Russia, Britain, France and Germany -- are however insisting that sanctions will only be suspended, not lifted.
Kerry's talks in Lausanne with Foreign Minister Mohammad Javad Zarif and officials from the six powers are aimed at agreeing the outlines of a nuclear deal by March 31 after two missed deadlines in 2014.
The two men met for more than four hours today, and their political directors were planning to resume talks later in the evening.
Such a deal, meant to be finalised by June 30, would see Iran downsize its nuclear programme to ensure that any covert dash for an atomic weapon would be all but impossible.
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