The pair were among 15 Royal Navy personnel held captive in Iran over claims they entered the Islamic republic's waters illegally.
Following their release last Wednesday and the subsequent interviews, the government has attracted criticism from all quarters for its handling of the situation.
Mr Browne stated that although he did not make the initial decision – soon withdrawn - to allow sailors to sell their stories to the press, he takes responsibility for it as a secretary of state.
Today, shadow foreign secretary and former Conservative leader William Hague accused Mr Browne of a grave mistake in initially endorsing the decision.
"This has been quite an important event," Mr Hague told the Today programme.
"It is not often that a minister manages to undermine the reputation of the armed forces, cut across a major inquiry and shatter the political unity of the country all in one decision."
Prime minister Tony Blair yesterday admitted that "with hindsight" the selling of the stories was not a "good idea" but Downing Street has refused to confirm whether Mr Blair was directly involved in the decision.
On this issue Mr Hague added: "It seems strange to us that No. 10 did not have greater involvement in this in this very centralised administration where No.10 are routinely consulted by all government departments.
"It seems very odd that the prime minister read of this in the Sunday papers when [Tory leader] David Cameron and [shadow defence secretary] Liam Fox and I all knew about it on Saturday."
Lord Ramsbotham, the former chief inspector of prisons and an ex-army general who once held the post of director of army public relations, also added his criticism today, joining other former senior officers in expressing their opinions.
"I cannot understand how the decision was taken in the first place and secondly I cannot understand how any minister allowed it," he told the Today programme.
And he agreed that Mr Browne was likely to face some tough questions when he makes a statement to the Commons on Monday.
"I have an awful feeling there's a bit of Easter weekend hanging over this story, that not everyone was necessarily there and therefore a decision taken by an admiral was, as it were, rubber-stamped without being properly checked," he said.
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