Trump posted on social media that the emerging agreement would reopen the strait, the vital shipping passage whose closure has upended global energy markets since the US and Israel launched the war on Iran in February. 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 the agreement would allow Iran to manage the strait and that Trump's assertion on the strait was "inconsistent with reality".
However, Axios reported - citing a US official - the US and Iran are close to signing a deal involving a 60-day ceasefire extension, during which the Strait of Hormuz would be reopened, Iran would be able to freely sell oil and negotiations would be held on curbing Iran's nuclear program.
The deal includes an "apparent commitment" by Iran to give up its highly enriched uranium, the New York Times reported, citing two unidentified US officials.
Details of how Iran would cede that stockpile would be left for a subsequent round of talks, the newspaper quoted the officials as saying.
While offering various war aims during the three-month-old conflict, Trump has repeatedly said the US 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.
Iran 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, which has sought to be a mediator in the war.
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".
Pakistani Prime Minister Shehbaz Sharif praised Trump on X 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 US accepts the memorandum, further talks could take place after the Eid holiday ends on Friday.
The US president, whose approval ratings have been hit by the war's impact on US energy prices, 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 spoke on Saturday with leaders from Saudi Arabia, Qatar, the United Arab Emirates, Jordan, Egypt, Turkey and Pakistan. The leaders encouraged Trump to agree to the emerging framework, Axios reported.
A call with Israeli Prime Minister Benjamin Netanyahu also went "very well", Trump wrote on Truth Social.
Pakistan has aimed to narrow differences between Iran and the US after weeks of war have left the vital Hormuz waterway closed to most shipping despite a nervous ceasefire.
"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 US blockade on its ports and the lifting of sanctions on Iranian oil sales.
Baghaei said the issue of the US blockade on Iran's shipping was important, but that its priority was ending the threat of new US attacks and the ongoing conflict in Lebanon, where Iran-allied Hezbollah militants are fighting Israeli troops who have moved into the south.
