The Prime Minister has warned that Parliament should be "wary" of passing legislation to regulate the press as recommended in the long-awaited Leveson report on media standards.
Lord Justice Leveson proposed a new independent press regulator, but said this should be underpinned by legislation guaranteeing its independence and effectiveness.
His report also calls for the broadcasting regulator Ofcom to "recognise and certify" that the new press regulator meets the requirements of the legislation.
While the proposal was greeted with broad agreement by the Labour and Liberal Democrat parties, David Cameron made it clear he had concerns, as our Political Editor, Tom Bradby reports.
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 on wayward publications.
Her told the House of Commons:
His response was in stark contrast to his coalition colleague Nick Clegg and the Labour leader Ed Miliband. Both threw their support behind Leveson's proposals with only a few minor concerns over detail.
He added: "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."
All three party leaders have spoken about their desire to work across party lines on the issue, and talks began as soon as the session in the House of Commons had finished.
If the disagreements persist, there is the prospect of a House vote on the issue - something Ed Miliband has said should take place before the end of January.
The Labour former cabinet minister Lord Mandelson accused Mr Cameron of putting the interests of politics before those of victims in his response to the Leveson inquiry.
He called Lord Justice Leveson's report a "very moderate, very realistic set of proposals" and urged the Government to implement them quickly.
The sweeping changes proposed in the Leveson report have united rival newspapers who are against Lord Justice Leveson's key idea. The Editor of the Independent told ITV News the outcome could have been harsher and others have questioned the idea that the broadcasting watchdog should oversee them.
Our UK Editor, Lucy Manning reports.