Under the deal announced Monday, the newspaper industry lost its power to veto appointments to the body that replaces the Press Complaints Commission, discredited because it didn't investigate phone hacking by leading newspapers, The Guardian reported Tuesday.
"It is a neat solution," Cameron said of the proposal. "It is not a panacea."
Cameron, quoting Labor Party lawmaker Gerald Kaufman, said it's "closing time in the last chance saloon. This replaces a failed regulatory system with one that will work because it has some real independence at its heart and is going to be properly overseen without allowing Parliament to endlessly interfere."
He said the new royal charter sets up the body to recognize the regulator but it remains a voluntary choice for the industry to decide whether to set up the system of independent regulation.
If newspapers refuse to cooperate with the regulator, or set up a panel unacceptable to the new recognition committee, the publications could be more liable for damages if they recklessly publish inaccurate stories, The Guardian said.
The prime minister's office said smaller, Web-based news providers, social networking sites and blogs would not be required to cooperate with the new regulatory system.
"This is a political deal between the [political] parties and Hacked Off," an advocacy group for those whose phones were hacked, one newspaper group executive said. "It is not a deal with the newspapers."
In a statement, Associated Newspapers, News International, Telegraph Media Group and Northern & Shell said they would seek "high-level legal advice" before deciding whether to join the new watchdog.
"No representative of the newspaper and magazine industry had any involvement in, or indeed any knowledge of, the cross-party talks on press regulation that took place on Sunday night," the statement said.
Associated Newspapers, News International and Telegraph Media Group had been considering a possible boycott of the regulator and establishing their own body if they think press freedoms are threatened, The Guardian said.
Notable deaths of 2014 [PHOTOS]