David Cameron agreed to produce a draft bill of the Leveson recommendations today, in a bid to demonstrate that the core proposal is "unworkable".
The report on media standards said a new independent press regulator should be recognised in law, probably through Ofcom.
That decision split the coalition yesterday, with Cameron opposing it and Nick Clegg joining Ed Miliband to support it.
"Our concern is that we simply don't need to have that legislation to achieve the end objectives," media secretary Maria Miller said.
"In drafting out this piece of legislation, what we are going to be demonstrating is that it wouldn't be a simple two-clause bill.”
She added: "What we are concerned about is creating amendable legislation that could in the future give a framework which could give parliament the opportunity of stopping reporting on certain areas. You have to consider that carefully before going forwards."
Miller was repeatedly asked whether she thought the report was "bonkers", given that Cameron had previously pledged to implement it in full unless its recommendations were "bonkers". She refused to answer.
Meanwhile, the reaction to the report fell along predictable lines, with newspapers rubbishing its proposals and victims of phone-hacking mostly praising it.
There were exceptions however. Guardian editor Alan Rusbridger welcomed "a bit of statute" to set up an arbitration arm in the new regulator, while Gerry McCann – father of missing child Madeline – criticised the report for not going far enough.
"Although we broadly welcome Lord Leveson's report and it has many merits, for me I don't think it has gone far enough," he said.
"I would have liked to see a properly independent regulation of the press whereas I think he's given them another chance at self-regulation."