Royal Marines boarded an oil tanker off the coast of Gibraltar on its way to Syria earlier this month.
Police in Gibraltar have arrested the captain and chief officer of the supertanker detained last week in an operation involving Royal Marines.
The move comes just hours after a Royal Navy warship drove off Iranian patrol boats as they attempted to impede the progress of a British tanker through the Strait of Hormuz.
The incidents come a day after Iranian President Hassan Rouhani warned of unspecified "repercussions" for the seizure of the Grace 1 tanker off Gibraltar on Thursday 4 July.
In London, ministers urged Tehran to "de-escalate" the situation in the Gulf.
But the arrest of the ship's officers of the Grace 1 in relation to suspected violations of EU sanctions on Syria is likely to exacerbate the already heightened tensions in the region.
In a statement, the Royal Gibraltar Police said the arrests followed a "protracted" search of the vessel, which remains in detention, during which documents and electronic devices were seized.
Earlier the Ministry of Defence confirmed the Type 23 frigate HMS Montrose had been forced to intervene when three Iranian fast patrols attempted to "impede" the passage of the BP-operated tanker British Heritage.