Instead the prime minister has scheduled a showdown vote in which MPs will be asked to support his alternative plan for a Royal Charter.
However both the Lib Dem and Labour leadership support the statutory underpinning of regulation as proposed by Leveson and as such Cameron does not have an obvious parliamentary majority on the issue.
Hacked Off called the failure to agree "a shameless betrayal of the victims of press abuse".
It is unclear whether Nick Clegg will tell his MPs to vote with Labour to defeat the Tory proposals, however it would be extremely awkward for the deputy prime minister to abandon his previous strong support for Leveson.
The outcome of the vote is made more uncertain as many Tory MPs are in favour of the Leveson plan, while some Labour MPs are opposed to it.
In a hastily-arranged press conference in 10 Downing Street, Cameron announced that the cross-party talks had "concluded without agreement" after a conference call between himself, Clegg and Ed Miliband this morning.
He said that the proposals for an independent body, established by Royal Charter, to oversee the system of press self-regulation would provide "the toughest regulation of the press that this country has ever seen".
Newspapers would refuse to sign up to a new system which is underpinned by statute, as recommended by Lord Justice Leveson and advocated by Labour, Lib Dems and the Hacked Off campaign group, he warned.
"The route I have set out is the fastest possible way to deliver the strong self-regulation body that Leveson proposed that can put in place million-pound fines, prominent apologises and get justice for victims in this country," said the prime minister.
"The deal is there to be done, it is the fastest way to get proper justice for victims."
And a senior Lib Dem source said that Cameron had made the decision to pull the plug on cross-party talks "unilaterally" and the Liberal Democrats were now considering their next step.
"We were very surprised and disappointed," said the source. "We thought we were making real progress and inching towards a deal, but the Prime Minister has unilaterally decided to pull the plug on cross-party talks.
"We are still prepared to work with politicians of all parties, including the Conservatives, who want to work with others to implement Leveson."
Asked whether Lib Dems would vote with Labour against the Royal Charter proposals on Monday, the source said: "We are going to have to talk about it and see what we do. Nothing has been agreed in government."
A senior Labour source said: "The prime minister's decision is very disappointing. We still hope for an agreement. We still believe there can be an agreement. We urge the Prime Minister to reflect on his actions."
Index on Censorship chief executive Kirsty Hughes backed the PM's move, and said he was right not to make a "shoddy compromise with Nick Clegg and Ed Miliband, which would have meant statutory underpinning of press regulation.
"A tough new independent regulator whether set up by Royal Charter, or preferably by a route with no political involvement at all, is a big step forward compared to the previous system of self-regulation.
"Cameron’s decision to go to a vote has clearly been forced by the threat of wrecking amendments being added into several bills, including one that is already threatening the passage of the Defamation Bill, which Leveson himself said should be kept separate from his work."
Professor Brian Cathcart, Executive Director, Hacked Off said Cameron had “chosen to throw his lot in with powerful national newspaper groups, whose actions were condemned in the Leveson Report.
“He allowed the newspapers to rewrite Leveson so much that they would have been able to pick and choose which complaints their self regulator dealt with and would have given the self regulator little power to tell a paper to give an apology or a correction due prominence.
“Worse than that, the editors would have been able to write their own rules and handpick the people who ran the regulator.
“Cameron is trying to raise a smokescreen to hide his dirty dealings behind closed doors with powerful press barons who don’t want to have to be accountable when their newspapers –to use Lord Justice Leveson’s words – ‘wreak havoc in the lives of innocent people’”.