Many of the tankers that have transited the strait in recent days have been linked with Iran following the lifting of the US naval blockade as part of the deal.

At least 30 tankers have departed from the Gulf laden with Iranian oil and petrochemicals since the deal was agreed, according to Jemima Shelley, a senior research analyst at the United Against Nuclear Iran campaign and monitoring group.

The US Treasury has also eased decades-old sanctions by issuing a license to allow the sale of Iranian crude oil, petrochemicals and other oil products until 21 August.

On Monday at least five tankers previously sanctioned by the US for links with Iran moved through the strait, ship tracking data shows, carrying up to four million barrels of oil.

"That said, there has been an increase in 'normal' trade too," said Martin Kelly of crisis management firm EOS Risk Group.

Four liquefied natural gas tankers were seen on ship-tracking platforms heading through the strait to Qatar's Ras Laffan port on Monday and at least three tankers and three cargo vessels sailed out of the Gulf on Tuesday.

All of these transits were made along the Iranian-approved northern route through Iranian waters, rather than the US-recommended southern route close to the coast of Oman.

And, according to ship-tracking data, more than 250 tankers and 440 cargo ships are still inside the Gulf, based on their last reported positions. More than 80% of the tankers are stationary or at anchor and about one in six appears to be carrying cargo.

Concerns about sea mines in the internationally recognised shipping lanes through the middle of the strait have also played a part in holding ship traffic back from its pre-war levels.

The Joint Maritime Information Center (JMIC), a multinational maritime group which includes the US, has warned ships to avoid this central part of the strait "due to the existence of mines".

So far, the JMIC has issued warnings and co-ordinates for two mines and said "active mine clearance operations are ongoing".

The JMIC has recommended vessels take a narrower southern route through the strait, closer to the coast of Oman, which it says "has been confirmed clear of mines".

"We saw tankers passing along the southern corridor at the end of last week and then when Iran declared the strait closed again on Saturday 20 June the transits stalled," said Shelley.

"There has been some resumption of tankers passing today but still only a trickle," she added.

At least four tankers appeared to be transiting the strait through the southern route on Tuesday, ship-tracking data showed, including a Norway-flagged ship sailing to Singapore and a Liberia-flagged vessel heading to Taiwan.

Additional reporting by Ghoncheh Habibiazad, BBC Persian