Downing Street has flatly denied any role in the decision to allow the navy crew freed by Iran to sell their stories to media.
Faye Turney's story was bought for a reported six-figure sum
No 10 also denied helping them negotiate with media outlets interested in their stories.
It follows accusations that the sailors had been used as pawns in an international propaganda war with Iran.
Conservative leader David Cameron had also called for Tony Blair to clarify what he knew about the sale.
Defence Secretary Des Browne has taken responsibility for the navy's decision. He said he had not been "content" with it but believed he had no choice under the rules.
"Clearly with hindsight... I could have made a different decision," Mr Browne said on Wednesday.
The prime minister has said allowing the sailors to sell their story to the media had not been a "good idea" but that he had not been involved in the decision.
But following continuing speculation on Thursday about Downing Street's role, a spokewoman said: "As has already been made clear, no one in Number 10 - either the press office or officials - had anything to do with decisions taken by the Navy regarding their personnel receiving payments for media interviews.
"In addition, no one in Number 10 had any involvement in the negotiations around those interviews."
The decision to allow the personnel to sell their stories has drawn criticism from opposition MPs, former military figures and the families of servicemen killed or injured in Iraq and Afghanistan among others.
Major General Patrick Cordingly, who commanded the Desert Rats during the 1991 Gulf War, said he believed the personnel were being used "almost as a propaganda tool".
Earlier on Thursday, Mr Cameron accused Downing Street of being in "complete confusion" over the sale of the stories.
"I think the prime minister has got to make absolutely clear when he knew about this whole issue but, to me, what matters for the defence secretary is he has to pass two tests.
"First, he has to show he still has the confidence of members of our armed services, who are working so hard for our country.
"And secondly he has to give a full account of himself to the House of Commons on Monday. And I think it is very important he does that."
Shadow Foreign Secretary William Hague earlier told BBC Radio 4's Today programme the affair had damaged the reputation of Britain's armed forces.
And former Army public relations chief Lord Ramsbotham also told the BBC that in his experience, everything "of some magnitude like this" was referred to Number 10.
Meanwhile, former navy officer Mike Critchley, of Warship World magazine, has started a petition on the Downing Street website calling for Mr Blair to "name and sack" the person responsible for the decision.
By Thursday evening, more than 1,000 people had signed it.
Only two of the 15 captured navy personnel sold their stories.
Arthur Batchelor, 20, the youngest of the British sailors to be held captive, told the Daily Mirror about his "nightmare" at the hands of his captors.
And Leading Seaman Faye Turney sold her story to ITV1's Tonight with Trevor Macdonald and the Sun newspaper - reportedly for a six-figure sum, some of which will go to navy families.
There has been a mixed response to the decision on websites used by members of the armed forces, with some supporting the sailors' decision to sell their story and others condemning it.
One contributor to Rum Ration, an unofficial navy website, wrote: "It is simply shocking - get captured and you make five times the average sailor's salary in one story. I'm sorry, welcome home, but you signed on the dotted line like all the rest. I am appalled - have some dignity."
The Royal Navy crew of sailors and marines were on patrol boats in the Gulf on 23 March when they were detained by Iran's Revolutionary Guard - the Iranians said they had strayed into its waters, which the British deny.