Trump said late on Saturday on his Truth Social platform that Iran and other Middle Eastern countries had asked for time to complete a deal that would lead to "the Immediate, Complete and Total" reopening of the strait and "an end to Iran's nuclear threat" but that Tehran must "rapidly make a DEAL."
As he returned to Washington from a weekend in New Jersey, Trump told reporters negotiations would begin on Monday afternoon but didn't provide details of where it would take place or who would be involved.
Asked if there was a deadline for Iran to come to an agreement, Trump declined to answer.
"Would I rather make a deal? I'm not looking to kill people because people die, a lot of people die, and we don't want that," Trump said in response.
Trump has repeatedly issued threats that he would escalate the war on Iran he launched along with Israel in late February, only to allow more time for talks, which have so far not led to a comprehensive deal.
Trump's apparent de-escalation after days of threats of new attacks from each side was the latest twist in the war.
Attacks have spread across the Gulf to the Red Sea and even a Mediterranean facility in Egypt.
Iran has largely closed the Strait of Hormuz, a conduit for 20 per cent of the world's oil and liquefied natural gas before the start of the war, causing energy prices to rise and stoking broader inflation.
Trump has argued that his stated goal of keeping Iran from gaining nuclear weapons justifies higher fuel costs in the near term, but the economic pain has put political pressure on him to find a way to end the conflict.
Oil prices were down more than four per cent in early trading on Monday.
Iran's Foreign Minister Abbas Araqchi held phone calls with his Saudi counterpart Prince Faisal bin Farhan and Pakistan's army chief Asim Munir to discuss diplomatic efforts, Iran's state media reported on Sunday.
The official Iranian news agency IRNA reported earlier that negotiations between Tehran and Oman over the Strait of Hormuz were in their final stages, citing Iran's Foreign Minister Abbas Araqchi.
Iranian Foreign Ministry spokesperson Esmaeil Baghaei said negotiations were focused on agreeing a new route through the strait, adding that it had "no link to the Strait of Hormuz being opened or closed. That is a separate discussion".
Last month Iran publicly rejected an Omani proposal, backed by Gulf states, to manage the strait they share. People familiar with the matter had told Reuters the plan included the collection of voluntary fees for using the strait.
Eli Cohen, Israel's energy minister and a member of Prime Minister Benjamin Netanyahu's security cabinet, said there was close security and intelligence co-ordination between Israel and the US on everything happening in the region.
"With or without an agreement, and regardless of any external commitments, if Iran attempts to renew its nuclear program or advance its ballistic missile industries, we will be there. We will take action, and we will strike."
Trump and Netanyahu met on Tuesday in Washington, with an Israeli official saying they had explored all possible paths to curb Iran's nuclear program, including diplomacy, economic pressure and force.
with Reuters and AP
