The Editors' Code of Practice Committee, which sets the guidelines which the Press Complaints Commission must enforce, has announced it will meet next Wednesday to discuss its response to the Leveson report.
Committee chairman Paul Dacre, who is also the Daily Mail editor, said:
Lord Justice Leveson has set us a number of challenges: our task is to address them as urgently as possible.
We very much hope Wednesday's meeting will lay the framework for a fresh approach to the Editor's Code which will answer concerns raised during the inquiry.
Among the 13 editors on the committee are the Daily Mirror's editor Richard Wallace, Geordie Greig, London Evening Standard editor, and The Sunday Times editor John Witherow.
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.