A cross-party deal for a new press regulator underpinned by statute appeared closer as Labour said it was "confident" reopened talks had secured the basis of an agreement.
The Prime Minister began last-ditch efforts to find an accord on Sunday as he faced a likely Commons defeat on the issue on Monday with around 20 of his MPs set to back a rival package put together by an alliance of his Liberal Democrat coalition partners and the Opposition.
A senior Labour source said: "After five and a half hours of talks in Ed Miliband's office which ended at 2.30am, we are confident we have the basis of an agreement around our royal charter entrenched in statute."
The Conservatives were represented at the meeting by Cabinet Office Minister Oliver Letwin - who has been the key figure for the party in months of Leveson talks - and they were also attended by the Labour leader, Deputy Prime Minister Nick Clegg and shadow culture secretary Harriet Harman.
A Commons showdown was set up by Mr Cameron when he dramatically ended negotiations to find a way to implement the recommendations of the Leveson Inquiry into phone hacking.
He had said using legislation would "cross the Rubicon" and endanger press freedom, but appeared to soften his stance over the weekend
While Number 10 sources said the statutory underpinning was "unnecessary and undesirable", Mr Cameron signalled that it was not "a big issue of principle".
The Prime Minister, who met Mr Clegg to discuss the issue on Sunday night, is not thought to have yet signed off on any agreement, however.
Labour said it expected details to be announced in the Commons later.