US President Donald Trump said that a deal with Iran to end the war in the Middle East could be signed Sunday, and that the strategic Strait of Hormuz would be "open to all" immediately after.

Iran had offered a different timeline earlier in the day, but nonetheless signalled an agreement was in the offing, as both the warring parties and their mediators expressed increasing optimism that weeks of halting negotiations were drawing to a close.

The leader of key mediator Pakistan said a deal was closer "than ever before".

The "finalisation" of this agreement is expected "within the next 24 hours", Pakistani Prime Minister Shehbaz Sharif said Saturday on X, adding that it will be signed electronically, without going into further detail or specifying what this would involve.

He said "technical level talks" are expected to follow next week.

A Pakistani foreign ministry statement also said the signing was planned for Sunday.

The momentum came in spite of fresh skirmishes in the Strait of Hormuz, which Iran has blockaded since early in the war, throwing global markets into turmoil.

"The Deal is scheduled to get signed tomorrow, and immediately after it is signed, the Hormuz Strait is OPEN TO ALL," a post on Trump's official Truth Social platform read on Saturday.

Since an April 8 truce paused the worst of the fighting, Trump has repeatedly insisted a deal was imminent, only for the wrangling to drag on.

Iranian foreign ministry spokesman Esmaeil Baqaei had said earlier on Saturday that the date of the signing was yet to be determined, but "it will not be tomorrow".

However, he added: "The possibility of this happening in the coming days cannot be ruled out."

The warring parties have nonetheless released conflicting information about the contents of the deal, as each seeks to show it emerged from the war with the upper hand.

- Hormuz drones -

Tehran has insisted it will maintain control over the Strait of Hormuz, a key maritime trade route for oil and gas shipments from the Gulf.

Since imposing its blockade, Iran has demanded vessels obtain permission from its armed forces before transiting the waterway, and has established a new body to oversee it and collect tolls.

The US has responded with its own blockade of Iranian ports.

The US military's Central Command said earlier Saturday Iran had "launched multiple one-way attack drones in an attempt to strike commercial ships transiting the Strait".

It added that "US forces have downed all of them in recent hours".

Iran's Foreign Minister Abbas Araghchi, in an interview with state television Friday, had said the deal on the table called for the lifting of the US naval blockade.

"The administration of Strait of Hormuz will no longer be the same as before," he added, calling the waterway one of Iran's "main instruments of deterrence".

The US has repeatedly said Iran remaining in control of the strait would be unacceptable, and Trump's post made no mention of tolls or other arrangements.

- 'Nuclear dust' -

Another key sticking point in the talks has been the fate of Iran's nuclear programme, particularly its stockpile of highly enriched uranium -- believed to have been buried by US strikes last year during a previous short-lived war.

Iran has long insisted its nuclear programme is peaceful and that it has a right to enrichment, but the United States, Israel and other Western governments suspect it of seeking a bomb.

Araghchi on Friday said the only way to deal with Iran's enriched uranium "is to dilute it inside Iran".

Trump, who has justified the war as necessary to prevent Iran from obtaining nuclear weapons, previously said the US would remove and destroy the uranium.

In Saturday's post, he said: "When all is calm, we will go in and get the Nuclear Dust... and downblend and destroy it, whether in Iran, or the United States."

"Hopefully, this process will all work out quickly, easily, and smoothly," he added. "If it doesn't, we have the ultimate alternative, hopefully never to be used again!"

Prime Minister Benjamin Netanyahu of Israel -- which launched the war in tandem with the US in February -- said Trump had promised him any agreement would include the removal of the enriched nuclear material.

In the streets of Tehran, there was scepticism the latest agreement would cross the finish line.

"I don't think there is any deal soon," said Saeed Sadeghi, 49. "I don't trust their word."

Fars news agency shared a video from Iran's northeastern city of Mashhad showing dozens protesting the deal outside a foreign ministry building Saturday.

It showed women in black chadors chanting "death to dishonourable Araghchi, the infiltrator", while waving red and black flags.