Tory leader David Cameron has said Defence Secretary Des Browne may have to resign unless he can show the armed forces have confidence in him.
Mr Browne is due to make a statement to the Commons
He told the BBC Mr Browne had to give a "full account" of why sailors held by Iran were able to sell their stories.
The defence secretary is due to report to the Commons on Monday.
The Lib Dems said Mr Browne had made a "terrible mistake", but Home Secretary John Reid called him "courageous to say we got this thing wrong".
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 accused the crew of straying into its waters, but the British say they were in Iraqi territory.
They were freed earlier this month and later allowed to sell their stories.
Mr Cameron, speaking on BBC One's Sunday AM, said Mr Browne had to "give a full account to Parliament and explain the actions his department and Number 10 took".
He added: "The second test is, does he retain the confidence of the armed services?
"If he can pass those two tests then he keeps his job. If he fails, then I think he has to go."
Earlier, Mr Browne said he took full responsibility for allowing the crew's stories to be sold.
Mr Reid told Sky News: "You take decisions every day of the week when you hold a great office of state...
"I think it was courageous [of Mr Browne] to say we got this thing wrong."
Mr Reid added that it would be wrong to "tarnish" the entire armed forces over the sale of the crew's stories.
Liberal Democrat president Simon Hughes told Sunday AM that Mr Browne would need "some fairly clever answers" when he makes his Commons statement and that he had made "a terrible mistake".
In the BBC interview, Mr Cameron also spoke of his "admiration" for Prime Minister Tony Blair and said he had done an "important job" by moving the Labour Party to the political centre ground.
He said: "I think it's very important that we don't have a left-right split where one party wants to re-nationalise everything in sight, taxes at 80%, that's quite in hock to the trades unions.
"I think those changes to make the Labour Party more friendly to the enterprise economy - it's still not friendly enough - those are important."
Asked whether he felt a glow of pride or a wince at being called the "heir to Blair", Mr Cameron said he winced at the suggestion and that there were fundamental differences in their approach to politics.
He said: "I admire the fact he was won three elections in a row - you can't, as a politician, not admire that.
"But to me our whole approach to politics is different.
"In the end, politics to me is either trusting big government - that's Blair - or actually trusting people, sharing responsibility with them and trying to create a more responsible society - that's me.
"It's an enormous difference."
Mr Cameron said he was confident the Conservatives could win the next general election, but admitted it was not "in the bag".
He said the party was "half-way up the mountain" but there was still "a long way to go".