Prime Minister David Cameron has warned that Parliament should be "wary" of passing legislation to regulate the press of the kind recommended in the long-awaited Leveson Report on media standards.

In a damning report, Lord Justice Leveson condemned decades of "outrageous" behaviour by newspapers, finding that elements of the press repeatedly acted as if its own code of conduct "simply did not exist", and "wreaked havoc with the lives of innocent people".

He proposed a new independent press regulator with "credible" rules and powers to enforce them, and said that this should be underpinned by legislation giving the statutory regulator Ofcom a role in "verifying" the independence and effectiveness of the new body.

Mr Cameron gave a broad welcome to Leveson's proposal for a regulator with the power to demand prominent apologies and impose fines of up to £1 million. But the Prime Minister cast doubt on Leveson's central recommendation that a new system of press self-regulation required a statutory underpinning if it was to command public confidence.

He told the Commons: "I have some serious concerns and misgivings about this recommendation. For the first time we would have crossed the Rubicon, writing elements of press regulation into the law of the land. We should, I believe, be wary of any legislation which has the potential to infringe free speech and a free press. In this House, which has been a bulwark of democracy for centuries, we should think very, very carefully before crossing this line."

Mr Cameron's lukewarm response to Leveson provoked criticism from a number of MPs, including Labour leader Ed Miliband, who called for legislation in the next session of Parliament to put Leveson's central recommendations on to the statute book by 2015. Mr Miliband said: "We should put our faith in the recommendations of Lord Justice Leveson that were delivered to us today. I am sorry that the Prime Minister is not yet there, but I hope to convince him over the days ahead that is where we should go."

The extent of division within the coalition Government over the future of press regulation was made clear in an address to the Commons by Deputy Prime Minister Nick Clegg - the first time since the creation of the coalition in 2010 when Conservative and Liberal Democrat ministers have given separate statements in the same debate.

After the first in a series of cross-party talks on Thursday evening, a senior Labour source said Mr Cameron had agreed to ask the Department for Culture, Media and Sport (DCMS) to draft a Bill to implement Lord Justice Leveson's recommendation. The source said the talks, lasting less than 30 minutes, were "frank and to the point" and that Mr Cameron's agreement to ask DCMS to do this work came after he was put under pressure by a "robust" Mr Miliband.

According to Labour, the Prime Minister insisted he had not ruled out legislation, while Mr Miliband said that a timetable was needed for the implementation of Lord Justice Leveson's recommendations. The source said that Labour will move for a vote in the Commons on implementing Leveson in principle by the end of January at the latest.

A 10 Downing Street source said: "Contrary to Labour's claims, the PM's position has not moved an inch. He has deep misgivings about statutory regulation. The exercise of drawing up a Bill will demonstrate how complicated it would be to introduce press laws. As the PM said in the House, we have done some similar work over the past few weeks to look at what clauses might look like, and they always end up being more complicated and far-reaching than first thought."