A potential memorandum of understanding (MoU) between Iran and the US includes an end to the war on all fronts, Tasnim news agency reported on Sunday.
This includes Israel's attacks in Lebanon, and Washington would also commit to waiving sanctions on Iran's oil during negotiations.
If the agreement is reached, the Strait of Hormuz will not fully return to its pre-war status; instead, the number of ships allowed to pass would be restored to pre-war levels within 30 days, according to Tasnim.
Iran, the news agency said, emphasises the enforcement of its sovereign rights over the Strait of Hormuz through various means, the details of which will be announced later.
Meanwhile, Iran insists on at least a partial release of its frozen assets, and a potential deal would also include a 60-day negotiation window on Iran's nuclear program.
Tehran also calls for the lifting of the US blockade of its ports, arguing that no changes will be made in the strait if the blockade remains in place.
Any changes to navigation and transit through the strategic waterway will also depend on the implementation of the US's other commitments in the memorandum of understanding, the report said.
US President Donald Trump on Saturday said an agreement with Iran to end the war was "largely negotiated" and awaited finalisation.
The breakthrough came after Pakistan army chief Asim Munir visited Tehran, his second visit in recent weeks.
A ceasefire in the war that started on February 28 was first mediated by Pakistan on April 8.
