Shell boss Ben van Beurden said today that the company was closely monitoring tensions in the Strait of Hormuz.
He said there were currently no Shell-managed, UK-flagged tankers in the area.
The UK-flagged Stena Impero tanker was seized by Iran in the Strait on July 19 amid worsening relations between London and Tehran.
The US and Iran are also at loggerheads after the Trump administration pulled out of an international nuclear deal and imposed sanctions on Iran.
A Royal Navy frigate had to intervene to stop Iran blocking a BP-operated vessel leaving the Persian Gulf.
BP chief executive Bob Dudley said earlier this week that the firm was avoiding sending British ships and crews through the waterway.
Mr van Beurden said today: “We are following the situation very closely for a number of reasons − for the care and safety of seafarers, and the protection of assets.
“We monitor every vessel individually and asses the conditions around it.
“There are still Shell-managed vessels in the Strait of Hormuz and that will continue to be the case. Currently, though, there are no UK-flagged vessels in the strait.
Mr van Beurden said UK-flagged vessels would be accompanied by the Royal Navy as a precaution.
He added: “We monitor closely with the navy. This is something that is at the top of our attention.”