John Whittingdale, the chairman of the Commons culture, media and sport committee, has said the proposals from the newspaper industry for a system of press regulation that rivals the approach backed by all thee main political parties were a "hugely welcome step".
He told The Huffington Post UK it would be "tragic" if an agreement between government and the press could not be reached and urged David Cameron to hold further negotiations with the industry.
"I think this is a hugely welcome step in that in publishing this version of the charter, basically the industry have accepted all the main requirements for an independent regulator," he said.
"I am very happy with the model the industry suggests, it is in fact based on the proposals which Oliver Letwin came forward with and I would hope now there are further discussions to try and over come those small differences."
The newspaper industry today firmly rejected the government's plans for the future of press regulation and published its own proposal for a Royal Charter to create a tough and independent new system of self-regulation.
The industry's rival charter would crucially not include the government's plan that the regulatory system could only be removed following a two thirds majority vote of both houses of parliament.
In a statement co-ordinated by the Newspaper Society, they said that the Royal Charter published by the Government on March 18 has been condemned by a range of international media freedom organisations and enjoys "no support within the press" in the UK.
"A number of its recommendations are unworkable and it gives politicians an unacceptable degree of interference in the regulation of the press," warned the statement.
Whittingdale said given the gap between the two plans was so small it would "tragic" and "disastrous" if an agreement could not be reached.
"I would hope the Conservative party and government view this as an extremely constructive move and now have further discussions," he said.
Whittingdale, who was also against the statutory underpinning of press regulation added: "If they have found a method which doesn't require the involvement of parliament then, hurrah."