David Cameron has backed the principles behind Lord Justice Leveson's recommendation for a tougher regulatory body for the press.
But he says he has "serious concerns and misgivings" over bringing in laws to underpin any new body.
In a first for the coalition, deputy PM Nick Clegg spoke after the PM and disagreed, saying such a watchdog was both "proportionate and workable".
Labour called the report "measured" and backed its conclusions "unequivocally".
Mr Cameron, Mr Clegg and Labour leader Ed Miliband met for the first in a series of cross-party talks, following the Commons debate.
A senior Labour source said Mr Cameron had agreed, during the 30 minute negotiations, to ask the Department for Culture, Media and Sport (DCMS) to draft a bill to implement Lord Justice Leveson's recommendation.
The source added that Labour would push for a Commons vote on implementing the recommendation in principle by the end of January. There is set to be a full Commons debate on Leveson on Monday.
In his 2,000-page report, Lord Justice Leveson said the press must create a new and tough regulator but it had to be backed by legislation to ensure it was effective.
He said the press had failed to properly regulate itself in the past, but he believed the law could be used to "validate" a new body.
Mr Cameron told MPs that legislation backing a regulatory body could "cross the Rubicon" by writing elements of press regulation into the law for the first time.
"The danger is that this would create a vehicle for politicians, whether today or some time in the future, to impose regulation and obligations on the press, something Lord Justice Leveson himself wishes to avoid," he said.
"I believe there may be alternative options for putting in place incentives providing reassurance to the public and ensuring the Leveson principles of regulation are put in place, and these options should be explored."
The prime minister said the press should be given a "limited period of time" to put a new system in place.
"While no one wants to see full statutory regulation, the status quo is not an option," he warned.
He added: "The real test is not whether this body is backed by statute or not.
"The real test is: Can it fine newspapers? Can it call editors to account? Can it get front page apologies?
"That's what people want to know and that's what we need to deliver."
However, the deputy prime minister, who gave a separate statement to MPs, said he disagreed with Mr Cameron and was prepared to back the regulatory system set out by Leveson.
"I understand the entirely legitimate reasons why some members of this House are wary of using legislation," he said.
"I have thought long and hard about this. I'm a liberal, I don't make laws for the sake of it - and certainly not when it comes to the press.
"Indeed, when I gave my own evidence to the inquiry, I made the point that, if we could create a rigorous, independent system of regulation which covers all of the major players, without any changes to the law, of course we should.
"But no one has yet come up with a way of doing that.
"Lord Justice Leveson has considered these issues at length. He has found that changing the law is the only way to guarantee a system of self-regulation which seeks to cover all of the press."
Mr Clegg did raise concerns about the report's recommendations on data protection and the suggestion that it should be Ofcom - which regulates the broadcast media - which independently verifies the new press watchdog.
Labour leader Ed Miliband said his party "unequivocally endorse both the principles set out and his (Leveson's) central recommendations".
He said: "After 70 years and seven reports which have gone nowhere, now is the time to act.
"The case is compelling. The evidence is overwhelming.
"This is a once-in-a-generation opportunity to make change the public can trust."