David Cameron, Ed Miliband and Nick Clegg are expected to meet again to discuss the Leveson press reforms after “good” talks today.
The party leaders held 45 minutes of discussions on proposals for a new system underpinned by a Royal Charter this afternoon.
A Labour source said: "It was a good meeting, but there are still issues to be resolved.
"The discussions will continue. The party leaders expect to meet again in the next few days."
The meeting came after Labour moved to ensure it will have the option of adding tough statute-backed reform into the Crime and Courts Bill next week.
Responding to pressure from the Opposition, Lib Dem home office minister Jeremy Browne gave assurances that there would be an opportunity to debate "Leveson-related amendments" on Monday.
The development means unless Mr Cameron makes progress on the issue he is likely to face a Commons vote - which he could lose as Labour and the Lib Dems join forces with some Tory backbenchers.
The progress of the Defamation Bill has already been halted after peers led by Lord Puttnam inserted a new clause which would set up a statutory oversight body for press regulation.
Lord Skidelsky has also tabled similar amendments to the Enterprise and Regulatory Reform Bill.
Sources played down the idea that the parties were on the verge of hammering out a deal.
Earlier, shadow communities secretary Hilary Benn told BBC2's Daily Politics: "It's really important, now we come to the crucial moment, that... if agreement can't be reached to implement full Leveson that Parliament can do it by means of a vote.
"In the end the Prime Minister has got to stick to the words that he said when Leveson was published."
Actor Hugh Grant - the phone-hacking victim who fronts the Hacked Off group campaigning for full implementation of the Leveson recommendations - said he feared an acceptable agreement was still "a long, long way" off.
"This will keep happening and the Government's legislative agenda will be completely screwed because no one will give up on this," he said of the move to open the Crime and Courts Bill option.
Grant said: "This is the will of the people and it is not right that a tiny rump of Conservatives who happen to be in the executive are doing the will of the press, who they desperately need to stay there because the rest of their policies have gone cock-eyed."
Liberal Democrat pensions minister Steve Webb said: "The goal is doing a full Leveson, that has got to be what we aim for, that is what the Liberal Democrats are trying to achieve.
"But the other goal which Leveson was in favour of is all-party agreement, because the last thing we want is Labour and the Lib Dems to gang up and get something through in this Parliament and then you have a future Tory government that comes in and says, 'we never signed up to that', and then the regulation of the press becomes a political football, and we don't want that."