Iranian intelligence officers told the 15 British captives they became suspicious about their activities after seeing an interview with one of them on British television.
Families of the hostages said their loved ones told them the Iranians made the claim soon after capturing them.
The revelation is likely
to raise questions about the Ministry of Defence decision to allow the media to accompany HMS Cornwall, on which the service personnel were serving, and report on its activities.
On 13 March - 10 days before the 15 were seized - Britain's Channel 5 television broadcast an interview with Captain Chris Air, one of the captured Marines, in which he said his crew's role was to liaise with Iraqi vessels to "let them know we are here to protect them, protect their fishing and to stop any terrorism or any piracy in the area".
The Iranian interrogators told their captives this alerted them to Cornwall's role.
But Channel 5 said it had taken care to edit its report so as not to jeopardise the frigate's activities or the safety of the hostages once they had been taken.
The full interview with Air was not given to the media until after the hostages had been released.
In the film held back, Air said the ship was collecting information on the Iranians from passing ships.
"It's partly a hearts-and-minds-type patrol," Air said. "Secondly, it's to gather int [intelligence] if they do have any information, because they're here for days at a time.
"They can share it with us, whether it's about piracy or any sort of Iranian activity in the area, because obviously we're right by the buffer zone with Iran."
The ministry confirmed at the weekend that the Iranians had claimed they became interested in Cornwall's activities after learning about the ship from British television.
But it denied that letting the ship's crew be interviewed while on active duty had jeopardised the mission.
"HMS Cornwall's activities in the north Arabian Gulf are legitimate and open," a ministry spokeswoman said.
The ship's presence in the area was well known.
"Details of her activities as part of the Combined Task Force 158 are published on both the MoD and Royal Navy websites.
"Also, as she is a Type 22 frigate, it would be hard to miss her physical presence."
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