The all-party draft's proposals were laid in Parliament yesterday as part of a Royal Charter on press regulation.
Culture Secretary Maria Miller said the deal would safeguard the freedom of the press and the future of local papers, but the industry said the proposals could neither be described as "voluntary or independent".
The proposals include a small charge for arbitration as an alternative to expensive libel courts, an opt-out for local and regional newspapers, and more involvement in decision making for the press and media industry.
However, head of the Society of Editors Bob Satchwell has warned it could mean "you wouldn't have a free press any longer".
Independent self-regulation is to be brought in after recommendations by the Leveson Inquiry following the phone-hacking scandal involving some British newspapers.
Satchwell, executive director of the Society of Editors, which draws its members from across the press and TV industry, told the BBC there were "key problems" with the charter.
"People in other countries, not just journalists, are looking at what's going on here at the moment with horror," he added.
The Industry Steering Group, which represents national, regional and local newspaper publishers, said it would "closely study" the politicians' proposals.
However, it said it was "impossible" to see that a regulator "imposed and controlled by politicians" would be "voluntary or independent".
Many in the press are keen to get their own regulator set up as soon as possible.
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