The audio message was accompanied by aerial video footage of a warship thought to be the HMS Montrose, which the UK defence ministry says has now been joined in Gulf waters by another warship, the HMS Duncan.
In the recording, an officer of Iran's Islamic Revolutionary Guard Corps guard is heard telling the Stena Impero to change course, adding: "You obey, you will be safe."
Iran seized the British-flagged tanker "Stena Impero" on July 19.
"British warship Foxtrot 236, this is Sepah navy patrol boat: you are required not to interfere in this issue," an Iranian naval officer can be heard saying in the recording aired on state TV.
An officer on board the warship responds: "This is British warship Foxtrot 236: I am in vicinity of an internationally recognised strait with a merchant vessel in my vicinity conducting transit passage".
The Iranian officer replies: "British warship Foxtrot 236, this is Sepah navy patrol boat: don't put your life in danger".
Iranian state television also released recordings of another incident on July 10.
"This is British warship Foxtrot 236, go ahead," a British naval officer can be heard saying.
His Iranian counterpart responds by saying: "British warship Foxtrot 236, this is Sepah navy warship... your tanker British Heritage under my control. You are ordered do not to interference in my operation."
Britain said on July 11 that three Iranian vessels attempted to "impede the passage" of the "British Heritage" commercial oil tanker in the Strait of Hormuz.
Tensions have been escalating in the region for weeks, with US President Donald Trump last month calling off at the last minute an air strike on Iran over its downing of a US spy drone.
Tehran has suggested the July 19 seizure of the Stena Impero was in retaliation for UK Royal Marines helping Gibraltar authorities detain an Iranian tanker in the Mediterranean Sea two weeks earlier.
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