The newspaper industry said the Royal Charter published by the Government in March has been condemned by a range of international media freedom organisations and enjoys "no support within the press" in the UK.
A statement co-ordinated by the Newspaper Society said: "A number of its recommendations are unworkable and it gives politicians an unacceptable degree of interference in the regulation of the press."
The industry's proposal is closely based on the draft Royal Charter published on February 12 following negotiations with national and local newspapers and magazines.
The statement described it as "a workable, practical way swiftly to deliver the Leveson recommendations, which the industry accepts, without any form of state-sponsored regulation that would endanger freedom of speech".
More top news
A medical tribunal found Dr Mark Bonar posed a "potential future risk of harm to patients".
After a lively start to the long weekend with torrential, thundery downpours - a drier night.
The bouncy castle, commissioned for the Common People festival, is taller than the Great Wall of China.