Representatives from the two sides met in Switzerland last weekend for talks to end the war, which resulted in the US partially lifting sanctions on Iranian oil exports.

The number of vessels crossing the Strait of Hormuz has risen significantly since the MOU was signed, according to maritime intelligence firm Kpler.

Its latest data suggests 284 vessels have made the transit from 18 June, the day after the deal was signed, although that is is still well below the pre-conflict average of some 138 crossings each day.

The ships passing through the waterway in recent days include those carrying crude oil, liquefied natural gas (LNG), fertiliser and other goods, Kpler told the BBC.

The US and Iran had also formed a “communication line” to prevent misunderstandings “with the aim of safe passage for commercial vessels through the Strait of Hormuz”, mediators Qatar and Pakistan said in a joint statement on Monday.

There has been a “tremendous shift” with far more ships using the strait in recent days, said Dimitris Maniatis, the chief executive of Marisks, a maritime risk advisory firm working with ships stuck in the region.

A limited number of ships can cross a northern passageway with the permission of Iranian authorities, he said.

The US navy has also provided guidance for vessels to travel through a southern route that is safe from mines and other obstacles that has been laid out since the war, Maniatis said.

But the number of ships crossing the strait is still below levels seen before the war, when it was used by more than 100 ships a day.

Hundreds of ships still appear to be waiting in the Gulf.