Sailors' story answers demanded
Ministers have come under renewed pressure over allowing
British sailors freed by Iran to sell their stories.
And an ex-Navy officer has started a petition on the Downing Street website calling for the person responsible to be named and sacked.
Mr Browne has said he was not "content" with the navy's decision but felt he had no choice but to back it.
"Clearly with hindsight... I could have made a different decision," the defence secretary said on Wednesday.
Prime minister Tony Blair has said allowing the sailors to sell their story to the media was not a "good idea" but said he had not been involved in the decision.
But Mr Hague told BBC Radio 4's Today programme it was "very odd" that Downing Street had not been more closely involved "in a very centralised administration where number 10 is routinely consulted by all departments".
He added: "The relationship of Downing Street to this decision has not yet really been established."
Former Army public relations chief Lord Ramsbotham also told the BBC: "My experience is that everything was referred to number 10 of some magnitude like this."
Mr Hague said allowing the sailors to sell their story had "shattered political unity" on Britain's policy towards Iran and "cut across" a Royal Navy inquiry into how the sailors were captured.
He stopped short of calling for Des Browne's resignation but said that might change if the defence secretary did not provide satisfactory answers in his statement on Monday.
"We need to know after that statement - we need to be able to assess - whether he commands the confidence of the people working under his political direction in the armed forces."BBC political editor Nick Robinson said it was unlikely Mr Browne would be sacked, because the prime minister, who is expected to resign after the May elections, was "not in a position to hire or fire anybody right now".
But, he added, the defence secretary may no longer be considered a "safe pair of hands" when it came to future Cabinet reshuffles.
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.
Both the Tories and the Liberal Democrats say more questions need to be answered about what safeguards had been put in place after a similar incident in 2004 when British servicemen were seized by Iran in the Shatt al-Arab waterway.
Liberal Democrat defence spokesman, Nick Harvey, told the BBC: "I think the government might be quite pleased that everybody's attention is focused on this issue of media handling and that some of the far bigger questions... have been rather conveniently left behind in the stampede."
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 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.
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