The Government is planning two pieces of legislation and a Royal Charter to provide legal backing for a new system of press regulation, campaigners have claimed.
The Hacked Off campaign said that the plan was outlined to them in a meeting with Culture Secretary Maria Miller and Cabinet Office minister Oliver Letwin.
Mr Letwin's proposals for a Royal Charter were discussed by David Cameron, Nick Clegg and Ed Miliband on Wednesday, though the three party leaders reached no agreement.
Hacked Off director Brian Cathcart welcomed ministers' apparent acknowledgement that legislation was needed to give the new press watchdog teeth, but said that the Government's proposals fell short of the recommendations of the Leveson report.
"It makes no sense for the Government to bin the carefully thought-through proposals presented by the judge, in favour of this rushed and over-complicated response," said Professor Cathcart.
It is understood that Mr Letwin envisages a verifying body to be set up under a Royal Charter, with the responsibility for ensuring the effectiveness of a voluntary system of self-regulation set up by the newspaper industry.
Prof Cathcart said ministers told him they plan two new pieces of legislation - one to underpin the verifying body and the second to put in place incentives for the press to join the self-regulation body.
It is understood that incentives could include the threat of exemplary damages or higher costs to be awarded in court cases against newspapers which fail to sign up.
Prof Cathcart said: "We are pleased to hear that ministers now acknowledge that legislation is necessary to ensure that a regulator is effective and truly independent of politicians and the press.
"However, the proposals as outlined are not what we seek, which is the full and prompt implementation of Lord Justice Leveson's recommendations, in the open and transparent manner he proposed."