(Corrects second bullet to specify Iran is disputing Trump's claim the strait could reopen)By Asif Shahzad, Michael Martina and Ryan Patrick JonesWASHINGTON/ISLAMABAD/NEW DELHI, May 23 (Reuters) - A "largely negotiated" memorandum of understanding on an Iran peace deal would reopen the Strait of Hormuz, U.S. President Donald Trump said on Saturday, although the Iranian Fars news agency disputed that claim.Trump posted on social media that the emerging agreement would reopen the strait, the vital shipping passage whose closure upended global energy markets after the conflict started in February when the U.S. and Israel launched strikes on Iran.He did not say what else would be included in an agreement."Final aspects and details of the Deal are currently being discussed, and will be announced shortly," Trump wrote on Truth Social.But Fars reported early on Sunday that the agreement would allow Iran to manage the Strait of Hormuz and that Trump's assertion on the strait was "inconsistent with reality."Iran had said on Saturday that it was working toward a memorandum of understanding on ending the war after its top officials met with Asim Munir, the army chief of Pakistan.The Pakistani army said the negotiations had resulted in "encouraging" progress. Two Pakistani sources involved in the talks said the deal being negotiated is "fairly comprehensive to terminate the war."A post on the X account of Pakistani Prime Minister Shehbaz Sharif praised Trump for his "extraordinary efforts to pursue peace."Sources have told Reuters the proposed ‌framework would unfold in three stages: formally ending the war, resolving the crisis in the Strait of Hormuz and launching a 30-day window for negotiations on a broader agreement, which can be extended.One of the Pakistani sources said that if the U.S. accepts the memorandum, further talks could take place after the Eid holiday ends on Friday.TRUMP SPEAKS WITH MIDDLE EAST LEADERSThe U.S. president, whose approval ratings have been hit by the war's impact on energy prices for U.S. consumers, said on Friday he would not attend his son's wedding this weekend, citing Iran among the reasons he planned to stay in Washington.Trump wrote on Truth Social that he had a phone call on Saturday with leaders from Saudi Arabia, Qatar, the United Arab Emirates, Jordan, Egypt, Turkey and Pakistan. Axios reported that the leaders encouraged Trump to agree to the emerging framework.A separate call with Israeli Prime Minister Benjamin Netanyahu went "very well," Trump wrote.Pakistan has aimed to narrow differences between Iran and the U.S. after weeks of war have left the vital Hormuz waterway closed to most shipping despite a nervous ceasefire.Trump has repeatedly said that the U.S. struck Iran to prevent it from obtaining nuclear weapons.Iran has denied it is pursuing nuclear weapons and says it has a right to enrich uranium for civilian purposes."The trend this week has been towards a reduction in disputes, but there are still issues that need to be discussed through mediators. We will have to wait and see where the situation ends in the next three or four days," said Iranian Foreign Ministry spokesperson Esmail Baghaei.Iran has demanded supervision of the strait, an end to the U.S. blockade on its ports and the lifting of sanctions on Iranian oil sales.Baghaei said the issue of the U.S. blockade on Iran's shipping was important, but that its priority was ending the threat of new U.S. attacks and the ongoing conflict in Lebanon, where Iran-allied Hezbollah militants are fighting Israeli troops who have moved into the south.Pakistan's army chief Munir left Tehran on Saturday after talks with Iran's top negotiator Mohammad Baqer Qalibaf and Foreign Minister Abbas Araqchi.Qalibaf said Iran's armed forces had rebuilt their capabilities during the ceasefire and that, if the U.S. "foolishly restarts the war," the consequences would be "more forceful and bitter" than at the start of the conflict.Despite weeks of conflict, Iran has preserved its stockpile of near-weapons-grade enriched uranium as well as missile, drone and proxy capabilities. (Additional reporting by Doina Chiacu, Ariba Shahid, Hatem Mater and Andrew Mills; Writing by Philippa Fletcher, Rod Nickel and Sergio Non; Editing by Kevin Liffey, David Gregorio, Nia Williams and Kim Coghill)