JERUSALEM/ISLAMABAD, April 17 -- Optimism grew on Thursday that the Iran war may be near an end, with a key Pakistani mediator having made a breakthrough on "sticky issues", a source said, although Iran warned the fate of its nuclear programme had not been resolved. The United States and Pakistan have been talking up the prospects for a deal in the more than six-week war, with US President Donald Trump saying the accord would open the crucial Strait of Hormuz, through which a fifth of the world's oil and gas supply flows. Closure of the strait has triggered the worst oil price shock in history and forced the International Monetary Fund to downgrade its outlook for the global economy, warning prolonged conflict could push the world to the brink of recession. Pakistan's army chief and a key figure in the mediation, Field Marshal Asim Munir, arrived in Tehran on Wednesday to try to prevent a renewal of the conflict after marathon talks held in Islamabad last weekend ended without a deal. A senior Iranian official told Reuters on Thursday that the trip had led to greater hopes for a second round of talks and an extension of the two-week ceasefire, but said fundamental differences remain over its nuclear program. Pakistan's foreign ministry said on Thursday that both sides are willing to resume talks, though no date had yet been set. Lebanon's president will not speak to Israel's prime minister in the near future, Lebanese officials said on Thursday, dealing a blow to US efforts to expand contacts between the enemy states as Pakistan said peace in Lebanon was vital to ending the Iran war. The US-Israeli war with Iran spilt into Lebanon on March 2, when Iran-backed Hezbollah opened fire in support of Tehran, prompting an Israeli offensive in Lebanon just 15 months after the last major conflict. "Peace in Lebanon is essential for (Iran) peace talks," Tahir Andrabi, spokesperson for Pakistan's Foreign Ministry, said. The Israeli security cabinet convened on Wednesday to discuss a possible ceasefire in Lebanon. President Donald Trump said on Truth Social he was seeking to create "a little breathing room" between Israel and Lebanon, adding the two leaders had not spoken for some 34 years and "it will happen tomorrow," in a post published late on Wednesday in Washington. But three Lebanese officials told Reuters on Thursday that President Joseph Aoun would not hold a call with Israeli Prime Minister Benjamin Netanyahu in the near future. Two of the Lebanese officials said the Lebanese embassy in Washington had informed the US administration of the position before a call between Aoun and Secretary of State Marco Rubio on Thursday. A brief Lebanese presidency statement said Aoun thanked Rubio for US efforts to achieve a ceasefire in Lebanon. "We feel good about the prospects of a deal," White House press secretary Karoline Leavitt said at a news conference on Wednesday, calling conversations mediated by Pakistan "productive and ongoing". She denied reports that the US had formally requested an extension of a two-week ceasefire agreed by the two sides on April 8. Mohammad Eslami, head of the Atomic Energy Organization of Iran, said talks needed to recognise Iran's rights, interests and dignity to be fruitful. "But if it continues, as it usually does, relying on deception and, in fact, on a lack of commitment and failure to adhere to agreements and set terms, then it naturally cannot succeed," he said during a pro-government rally in Tehran....