Culture Secretary Maria Miller appeared to indicate that the cross-party Royal Charter on press regulation passed this week could be redundant.
The main newspaper and magazine industry trade bodies have rejected the Royal Charter and are pressing on with the creation of the Independent Press Standards Organisation, a body which is instead set up under a system outlined in a publisher-backed Royal Charter which was rejected by the Privy Council.
Miller told the BBC Andrew Marr show that the best way to "stave off" statutory regulation was for publishers to create an effective system of self regulation.
Asked if "nothing else needs to happen" if IPSO works, she replied: "Yes. Ultimately yes there are opportunities for the press to be able to be recognised and I would encourage them to look at that because it does mean that they can get the sort of incentives around costs and also exemplary damages."
Told by Andrew Marr that this was likely to infuriate press reform campaigners, she said: "I think they need to examine what Lord Justice Leveson actually said. He said very clearly that a sign of success would be to have a system where we could take both the public and the press with us and that's been at the heart of the way I have approached this. And I do hope that the press see the charter as an opportunity for them to really demonstrate to the people who read their newspapers that they take responsibility very seriously indeed in terms of what they print, the way they print it and when errors and mistakes are made, that they have a system of redress in place."
Under a law underpinning the Government Royal Charter, publishers face exemplary damages and increased costs in libel and privacy cases if their regulator is not okayed by the recognition body which the charter sets out.
So publishers have to decide whether to change IPSO in order to fall in line with the Government charter or else run the risk of the increased costs.
Comedian and press reform campaigner Steve Coogan said of newspaper publishers: "I think the behaviour at the moment is like a recalcitrant teenager who keeps shouting 'it's unjust, it's unfair', when all you have asked him to do is tidy his bedroom."
Tory David Davis, former shadow home secretary, warned, however, that provisions that allow the royal charter to be changed with a two thirds majority in Parliament, as well as backing from the recognition board, would pave the way for political interference.
Writing in the Mail on Sunday he said: "In July, the Government forced Guardian staff to destroy hard drives containing the Snowden files.
"David Cameron claims they did this because they agreed the files posed a danger to national security. That is not true."
He added: "Last week Mr Cameron also warned newspapers that they must demonstrate 'social responsibility' or it would be very difficult for Government to stand back and not to act'.
"This is why we cannot trust this or any future government with press regulation. The supposed safeguards for press freedom might look strong now, but they can be swept away in an instant on the grounds of 'national security'."
Publishers' body the Press Standards Board of Finance this week failed to get an injunction stopping the Royal Charter from receiving the Royal Assent. It plans to take its case for judicial review to the Court of Appeal arguing that its own Royal Charter on press regulation was not given proper consideration.
No publisher has yet given its backing to the idea that press regulation should be underpinned by the Government's Royal Charter. The IPSO scheme which publishers favour currently falls down on meeting the detailed requirements of the Royal Charter in a number of areas but mainly in terms of independence from the industry and the compulsory provision of a libel arbitration service.
The Independent, Financial Times and The Guardian have also raised concerns about the independence of IPSO and are all understood not to have signed up to it yet.
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