The petition's 2,909 signatories are among a growing number of voices unhappy with the decision to permit the 15 sailors and marines to talk to the media when their 13-day ordeal ended on April 4th.
"We the undersigned petition the prime minister to name and sack the person responsible for declaring that members of the armed services can sell their stories to the media," the online petition states.
It goes on to dub the decision a "major government failure and a [public relations] disaster for the Royal Navy".
"Heads should roll at the highest level," it concludes.
But Downing Street said in response that Mr Blair has already recognised the navy was "trying to deal with a wholly exceptional situation".
"He has no intention of engaging in a witch-hunt against people who acted honourably and in good faith in very difficult circumstances," the statement added.
Defence secretary Des Browne has already admitted that the Ministry of Defence's stance was "in hindsight… not a good idea".
Two of the 15 sailors had already spoken to the press by the time Mr Browne reacted to growing criticism by issuing a temporary ban on all armed services personnel from selling their stories to the media.
Leading Seaman Faye Turney, the only woman among the captured group, gave interviews to the Sun and ITV1's Tonight with Trevor McDonald, while Able Seaman Arthur Batchelor spoke to the Daily Mirror.
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