Cameron and Rouhani discussed the recent improvements in bilateral ties between London and Tehran, the conflict in Syria and the latest round of negotiations over Iran’s nuclear programme, it said in a statement.
The last British prime minister to speak to an Iranian leader was Tony Blair, who called president Mohammad Khatami in 2002, a Downing Street spokeswoman told AFP.
“The prime minister became the first British prime minister to call the Iranian president in more than a decade today when he spoke to President Rouhani this afternoon, ahead of this week’s nuclear negotiations in Geneva,” a Downing Street spokesman said in a statement.
They “agreed to continue efforts to improve the relationship on a step by step and reciprocal basis” following the appointment of non-resident charge d’affaires to each others countries last week, the statement said.
The appointment of the envoys was a key step towards improving ties severed after Iranian protesters ransacked the British embassy in 2011.
The two leaders also discussed the talks between world powers and Iran on Tehran’s nuclear programme, the next round of which starts in Geneva on Wednesday.
“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 underway tomorrow,” the statement said.
Cameron “underlined the necessity of Iran comprehensively addressing the concerns of the international community about their nuclear programme, including the need for greater transparency”, it said.
“On Syria, there was agreement on the need for a political solution to end the bloodshed,” the Downing Street statement said.
Cameron also offered condolences over the double suicide bombing outside the Iranian embassy in Beirut earlier Tuesday, the Downing Street spokeswoman said separately.
The attack, claimed by an Al-Qaeda-linked group, killed at least 23 people.
“The prime minister talked about all of us taking a firm stand against terrorism. Terrorism is never right,” the spokeswoman told AFP.
