It would be "very regrettable" if newspapers tried to challenge cross-party plans for a new system of press regulation through the courts, Labour deputy leader Harriet Harman has said.
Ms Harman said that the industry should not seek to boycott plans to establish a new regulatory system through a royal charter passed by the Privy Council.
The representatives of the three main parties agreed a series of changes to the proposed charter intended to make it more palatable to the industry and encourage newspapers to sign up.
But a newspaper industry steering group last night made clear that the amendements failed to meet their fundamental objections, saying it was neither voluntary nor independent.
"This remains a charter written by politicians, imposed by politicians and controlled by politicians. It has not been approved by any of the newspapers or magazines it seeks to regulate," it said.
There have been reports that there could now be a legal challenge to the decision earlier this week by the Privy Council to throw out an alternative charter put forward by the industry.
However, Ms Harman, who represented Labour at the cross-party talks, said the press should now accept the verdict of the politicians and not try to challenge it through judicial review.
"I think it would be very regrettable because I think that it would be much better for them just to join in to the framework that has already been set forth. It's no danger to them at all," she told the BBC Radio 4 Today programme.
"For them to boycott it and say 'We are going to set up our own system' ... I think leaves us exactly where we were before which is the press are marking their own homework."
The latest text - amending the charter controversially agreed last March in late night talks with the parties and the Hacked Off campaign group - will now go forward for final approval by the Privy Council on October 30.
The steering group statement however increases the prospect that much of the press will simply go ahead with its own system of self-regulation, despite the threat of exemplary damages in any legal action newspapers are involved in if they remain outside the official system.
The Guardian columnist Jonathan Freedland said there were concerns within the industry that a regulatory system backed by royal charter could be used to clamp down on press freedom.
He highlighted the speech by the head of MI5 castigating his newspaper for publishing leaked details of the operations of GCHQ and its American counterpart, the National Security Agency.
"What worries me is the idea that under a system where there is a royal charter overseen by the Privy Council - which we all know is the body used for the state's most secrety business - there would be a mechanism for the head of MI5 not just to complain in a speech but actually to prevent that kind of publication," he told the Today programme.
However Ms Harman insisted that a measure in the charter requiring any future changes to be approved by a two-thirds majority of both Houses of Parliament - which some in the press fear could be used to toughen up the system of regulation - would safeguard against such interference.
"It makes more difficult for Parliament to change a charter and it makes it impossible for ministers to go shimmying into the Privy Council and, behind closed doors, toughen up and change the charter," she said.
"So it is a protection for the press. It is to prevent tampering - it is an anti-tampering device."