More cross-party talks on implementing the recommendations of Lord Justice Leveson will take place on Monday, but below party leader level.
Culture Secretary Maria Miller, her Labour shadow Harriet Harman and Lord Wallace for the Liberal Democrats will take part in the talks.
A man who won libel damages after his arrest over the murder of a woman has written to MPs asking them to back Leveson's recommendations.
About 2,000 editors will sign up to a new independent press watchdog, the chairman of the Press Complaints Commission has said.
The Prime Minister has taken a political gamble by holding differing views to the victims, the Leveson inquiry and a majority of MPs.