Culture secretary Maria Miller has insisted the "principles" of Lord Justice Leveson's press regulation blueprint can be met without giving it statutory backing.
She dismissed the question of legislation - which has put David Cameron on a collision course with his coalition partners as well as Labour and the victims of press intrusion - as "a matter of detail".
Lord Justice Leveson condemned the "culture of reckless and outrageous journalism" that dominated sections of the press for decades, as he unveiled the findings of his 16-month inquiry on Thursday.
The Appeal Court judge called for a new watchdog with statutory underpinning to be given the power to require prominent apologies and impose fines of as much as £1 million.
Cameron immediately voiced "serious concerns and misgivings" about legislative action, and said the press should be given "a limited period of time" to show it could get its house in order.
But deputy prime minister Nick Clegg said he believed the Leveson model could be "proportionate and workable" and Labour leader Ed Miliband urged MPs to "have faith" in the proposals.
The three leaders met for initial talks on Thursday night but consensus appeared distant.
Miller told the programme: "The horrific experiences of the McCanns and others cannot be allowed to happen again and that is why we are absolutely clear that we fully accept the principles of Leveson but, as you would expect, we would look at the details of implementation.
"We have some grave concerns about the principle of putting into place statutory underpinning for this new self-regulatory body but we are also not convinced that it is absolutely necessary to achieve the objectives that both Lord (Justice) Leveson set out and indeed the victims have set out."
She declined repeatedly to say whether she believed the statutory underpinning recommendation was "bonkers" - the test previously suggested by Mr Cameron for whether he would implement any proposed reforms.
"What we are absolutely doing is going to move forward with the core recommendation of the Leveson report, which is an independent self-regulatory body," she said.