Iran and the US said ships had again started moving through the Strait of Hormuz — with US President Donald Trump saying the vital oil route would be "completely open" by Friday — yet who will manage it and how remains unclear.

The reopening of one of the world's most important energy chokepoints is the crucial element in ending months of deadly war and economic turmoil triggered by US-Israeli strikes on Iran in late February.

After both Washington and Tehran announced a deal to end the Iran war on Sunday, questions have emerged over Hormuz's future, despite the US president's apparent optimism, who called on "ships of the world" to "start their engines" and "let the oil flow".

Yet Trump said overnight on Tuesday that "ships are starting to move, many loaded up with oil, out of the Strait of Hormuz," adding later that he did not think the US "will need much help" keeping the waterway open.

Iranian media seemingly confirmed Trump's claims, reporting on Monday evening that three oil tankers and two laden cargo ships had passed through the area that had been subject to a US naval blockade.