The royal charter passed earlier this week to regulate the press could become redundant, the Culture Secretary Maria Miller has indicated.
Industry leaders have railed against the plans it enshrines to establish a recognition body overseeing a new press watchdog and are pus hing ahead with the creation of an Independent Press Standards Organisation (IPSO) without any formal verification.
Mrs Miller told the BBC Andrew Marr show the best way to "stave off" the statutory regulation that many campaigners had wanted was 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 that 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."
Publishers who refuse to sign up to a system underpinned by the politicians' charter face exemplary damages in any court action they are involved.
Evening Standard editor Sarah Sands told the programme: "It sounds to me as if we are getting to a breakthrough."
Comedian Steve Coogan, one of the most high profile press reform campaigners, said the impasse on reforms had become a "war".
He told the programme: "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.
In the Mail on Sunday, he wrote: "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'."