The discussions are a result of the phone hacking scandal that came to a head in the summer of 2011, in which reporters -- mostly reporters at the now closed News of the World tabloid -- were discovered to be hacking cellphones of celebrities and others to get scoops.
The newspaper was closed as a result of the scandal, which has cost Rupert Murdoch's News Corp. hundreds of millions of dollars, The New York Times reported Thursday.
More than 100 reporters, editors and executives have been touched by the affair, including six former The News of the World employees who were arrested in February on suspicion of hacking, the Times said.
In arguably the most publicized event, the phone of a kidnapped girl, Milly Dowler, was hacked. The victim was later found to be murdered.
On Thursday, Cameron said he would pursue a Royal Charter for a new, self-regulating body that would have the power to levy fines and compensate victims of privacy abuses. The industry already has a self-regulating authority, but critics have said it is weak and favors a reckless style of journalism.
A Royal Charter is a legal entity that is used to set up organizations, such as the Bank of England and the British Broadcasting Corp., the Times said.
But the breakdown in talks could force political allegiances to shift, the newspaper said. The Liberal Democrats, who are aligned with Cameron's Conservative Party, could now support a different course of action along with the Labor Party.
"We were very surprised and disappointed. We thought we were making real progress and inching toward a deal, but the prime minister has unilaterally decided to pull the plug on cross-party talks," said an unidentified official with the Liberal Democratic Party.
But Cameron said he was standing his ground on having a system that was self-regulated.
"There's no point in producing a system that the press won't take part in. As prime minister, I wouldn't be fulfilling my duty if I came up with something knowing that it wouldn't work," Cameron said.
Notable deaths of 2014 [PHOTOS]