US President Donald Trump said Saturday that a deal with Iran to end the war in the Middle East would be signed on 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 new 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," Trump said on his Truth Social platform.

Since an 8 April truce paused the worst of the fighting, Trump has repeatedly insisted a deal was near 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".