Trump's hopes for an Iran peace deal come with caveats

But expectations were soon tempered by the US president himself.

Iran said on Wednesday it was reviewing a new proposal from Washington, after US media cited unnamed American officials as saying that the two sides were closing in on a one-page memorandum to end the war in the Gulf.

But hours after posting on Truth Social on Tuesday evening that he was suspending Project Freedom to see whether "the Agreement can be finalized and signed", Trump abruptly changed tone.

He said on Wednesday morning that an Iran deal was a "big assumption" and if it was not agreed, bombing at "a much higher level and intensity than it was before" would resume.

The president's threat came less than 24 hours after US Secretary of State Marco Rubio said at the White House that Operation Epic Fury, the American-led military strikes on Iran, was over.

Later on Wednesday morning, Trump expressed optimism in a brief telephone call with PBS about an Iran deal, while acknowledging it had previously proven elusive.

"I felt that way before with them," he said. "So we'll see what happens."

Trump also told PBS it was "unlikely" he would send US envoys for a second round of Iran peace talks in the Pakistani capital Islamabad.

The plan would reportedly aim to bring hostilities to a close, which would then be followed by discussions to unblock the Strait of Hormuz, lift sanctions and curb Iranian's nuclear ambitions.

But Axios also reported scepticism among some US officials about a deal and who would even approve such an agreement among the factions in Iran's leadership.

Iranian parliamentarian Ebrahim Rezaei, a spokesperson for Iran's National Security and Foreign Policy Commission, wrote on X that the 14 points reported by Axios amounted to a US "wish list".

He added that Iran "has its finger on the trigger and is ready" if the Americans did not "grant the necessary concessions".

In the US, foreign policy experts injected a note of caution, too.

"But we have been here before, and we've seen negotiations collapse at the last minute for a variety of reasons," added Rumley, now a fellow at the Washington Institute for Near East Policy.

Trump has repeatedly suggested a deal was close since a ceasefire was announced on 7 April.

On 17 April, he told CBS that Iran had "agreed to everything" and would allow the US to remove its enriched uranium – a claim officials in Tehran rejected outright.

In the White House on Wednesday, Trump again maintained: "They want to make a deal, they want to negotiate."

"And we'll see whether or not they are agreeing," he added.

During the Obama administration, it took over 20 months for the finer details of a deal on Iran's nuclear programme to be ironed out.

Shipping experts said that Project Freedom, which was announced on Sunday, had a limited impact in its opening hours, with only a handful of ships passing through the strait.

"There is no real policy process in this administration," he said. "The president makes decisions based on impulse more than process, therefore there are inconsistencies that happen all the time."

Mick Mulroy, a former assistant undersecretary of defence for the Middle East at the Pentagon, said any link between pausing Project Freedom and a possible peace deal remains murky.

"It's unclear if the pause in Project Freedom was because of this one-page memorandum or because the 1,500 ships currently stuck behind the [Strait of Hormuz] wouldn't transit even with the US security umbrella," he said. "Iran is likely trying to determine that as well."

The two leaders have a strained relationship and will be closely watched for signs of a breakthrough over tariffs and other issues.

The shooting took place near Arcadia Lake, in Edmond, at around 21:00 local time on Sunday, police say.

Airlines have cut 13,000 flights globally in May as jet fuel prices soar due to the conflict in the Middle East.

Reports have raised hopes of an agreement between the US and Iran after days of escalation.