Editors have railed against plans to establish a recognition body overseeing a new press watchdog and want to create an Independent Press Standards Organisation (IPSO) without any formal verification.
Culture Secretary Maria Miller said the best way to "stave off" statutory regulation 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 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.
"I do hope 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."