Representatives of most major national newspapers announced they would reject the plan agreed last month by the three major political parties in the aftermath of the Leveson inquiry, and instead published an alternate vision for press regulation.
Telegraph Media Group, Daily Mail publisher Associated Newspapers, and News International were behind the move.
The new plan is similar to the government’s proposal to set up a regulator backed by a Royal Charter. But it removes contentious clauses that would hand parliament ultimate control over the remit of the new body.
The industry said that under their plan the regulator would still be able to issue fines of up to £1m, would have a majority of independent members, and be able to request prominent corrections.
Dominic Mohan, editor of The Sun, said he supported a tough new system but insisted journalists should not be “censored by a state-sponsored Ministry of Truth”.
David Cameron’s spokesman said the Prime Minister would consider the new plans in due course.
The government’s plan, waved through parliament on 18 March, was agreed following a late night meeting between Conservative minister Oliver Letwin and Labour leader Ed Miliband.
Controversially, the final draft rested heavily on the proposals of the Hacked Off campaign group, who were present during the final discussions.
Last night the organisation said the latest proposals were a “desperate move” and accused the newspapers of “threatening to set up a new regulator of their own that will inevitably be another industry poodle like the discredited Press Complaints Commission.”
A spokesman for the Department of Culture, Media and Sport called on newspapers to back the deal passed by parliament: “The Privy Council Office will need to look at this proposal. We have already set out a draft Royal Charter which has cross-party agreement.”