Speaking on a trip to Wales, the prime minister's comments to reporters directed criticism at the Royal Navy rather than specifically at his embattled defence secretary Des Browne.
"The families were being pursued by the media to sell their stories. The Navy took the view that it was to manage the situation rather than let it happen. Now, with hindsight, was that a good idea? No," Mr Blair said.
His comments came after Mr Browne earlier admitted that "the buck stops here".
After the Conservatives yesterday called on Mr Browne to explain how the government allowed the sailors to speak out, the defence secretary today explained how he and the Royal Navy had felt uneasy with their recommendations over the weekend.
"They felt they had to make this decision but were not content with it," he said, explaining in a television interview that he felt the same way.
"On Monday when I was able to take advice from senior officials and from senior officers and had an opportunity myself to consider the regulations, I came to a different view… so clearly in hindsight I could have made a different decision," he added.
Conservative leader David Cameron told reporters while visiting service personnel in Scotland that the MoD needed to "make sure as far as possible that this doesn't happen again".
He called for a full public MoD inquiry, accountable to parliament, "so that we can learn the lessons of what went wrong" and said an explanation of the "calamitous decision" made by government ministers to allow the release of the stories was urgently needed.
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