The Conservative Party leader on Thursday abandoned discussions with Deputy PM Nick Clegg, leader of the Liberal Democrat junior coalition partners, and opposition Labour leader Ed Miliband.
Bringing the matter to a head, Cameron said lawmakers would vote on Monday on his proposals for a new newspaper watchdog.
But Labour and the Lib Dems want statutory regulation as recommended by the Leveson Inquiry, which Cameron commissioned in 2011 after the voicemail hacking scandal at Rupert Murdoch's now defunct News of the World tabloid.
Cameron believes underpinning the system in legislation would pose a risk to press freedom.
Cameron said on Saturday that he was "delighted" at how close together the two sides had come before he dramatically pulled the plug on talks.
And he said the Lib Dem-Labour proposed statutory underpinning was not "a big issue of principle".
"I think we're in a much better place and I'm confident about the future," he said.
"We're now in sight of getting that regulator with million-pound fines and proper regulation in our country.
"The idea of a law, a great big all singing, all dancing media law that would have been bad for press freedom, bad for individual freedom—that's off the table."
Cameron said he is asking lawmakers to vote for his plans for a royal charter—a special document used to establish organisations including the BBC and the Bank of England.
The move is a big gamble as he will find it hard to get it through Parliament in Monday's vote, an outcome that would deal a further blow for a prime minister struggling with a weak economy and divisions within his party.
Miliband on Sunday urged lawmakers to "stand up for the victims" of press abuse by enshrining a new press regulator in law.
"Monday is the day that politics has got to do the duty by the victims and has got to stand up for the victims," he told the Observer newspaper.
"It is an important moment because we have had decades of failing to ensure that we have a system of press complaints and redress which means that ordinary people aren't left at the whim of a sometimes abusive press."
Actor Hugh Grant, one of the main figures in the Hacked Off group which campaigns against press intrusion, said Cameron faced defeat on Monday because he was "so clearly on the wrong side in this".
"When he was forced to choose between honouring his promises to the victims of years of press abuses or staying cosy with the owners of Conservative-supporting newspapers, he chose the press barons," he wrote in the Observer.
"I hope that Parliament will grab this opportunity to recast the relationship between the citizens of Britain and their newspapers.
"If MPs fail, we will all be back here in 10 years' time with another inquiry after more newspaper abuses of innocent people." - AFP. .