David Cameron put in a call to Hassan Rouhani on Tuesday afternoon, marking the first time a British Prime Minister and an Iranian President have spoke in more than a decade.
The call came as Iran made fresh conciliations over its right to enrich uranium during negotiations with this US. The call marks a thawing of relations between Tehran and London ahead of further talks over the nuclear questions, which are scheduled to take place next week in Geneva.
"The two leaders discussed the bilateral relationship between Britain and Iran welcoming the steps taken since President Rouhani took office, including the appointment of non-resident Charges d'Affaires last week, " a Downing Street spokesman said.
"They agreed to continue efforts to improve the relationship on a step by step and reciprocal basis. On Iran's nuclear programme, both leaders agreed that significant progress had been made in the recent Geneva negotiations and that it was important to seize the opportunity presented by the further round of talks which get under way tomorrow.
"The Prime Minister underlined the necessity of Iran comprehensively addressing the concerns of the international community about their nuclear programme, including the need for greater transparency."
More from the Press Association:
Three days of high-level talks between representatives from Iran and the P5+1 group of nations earlier this month failed to achieve a breakthrough. US Secretary of State John Kerry said Iran been unable to accept a deal "at that particular moment", but Tehran blamed divisions between Western powers.
Some reports suggested France had wanted to place restrictions on the heavy-water reactor being built at Arak. Iran stresses that its nuclear programme is for peaceful purposes only, and has warned world powers against making "excessive demands" when trying to negotiate a deal.
TOP STORIES TODAY