Plans to create an independent press regulator backed by royal charter will be set out on Tuesday by the Conservatives.
Labour and the Liberal Democrats have backed the statutory underpinning of media laws proposed by Lord Justice Leveson following his inquiry into media ethics. But David Cameron has opposed the move, which he has claimed would "cross the Rubicon".
Oliver Letwin, the Cabinet Office minister, will detail the Tories' alternative proposals tomorrow.
All-party talks on the issue will take place on Thursday. The Liberal Democrats are understood to be sympathetic to the Letwin plan, although Labour remains hostile.
The subject has been given fresh impetus by a Lords vote last week calling for the creation of an arbitration service for people who felt wronged by a newspaper.
The Government now has to decide whether to overturn the vote when it comes before MPs or to accelerate efforts to reach all-party agreement. An opinion poll published yesterday showed that more than half of voters think a new system of press regulation should be backed by law.
Some 53 per cent felt statute was necessary if the new regime was to be effective and independent, while 23 per cent thought legal backing would put at risk the freedom of the press, the YouGov survey for the Media Standards Trust found.
Asked whether Lord Justice Leveson's proposals for reform – which included legislation – should be implemented, almost three-quarters (74 per cent) said they should, while 9 per cent said they should not.