More than 40 Conservative MPs - including several former Cabinet ministers - have urged Prime Minister David Cameron against adopting a new system of media self-regulation.
In an open letter in The Guardian, they reject the newspaper industry's plan for tougher self-regulation in response to the Leveson Inquiry into media ethics.
Senior party figures, including former foreign secretary Sir Malcolm Rifkind and two former party chairmen, Caroline Spelman and Lord Fowler, are among the group of Tories calling for much tougher reforms.
They said the Leveson Inquiry represented a "once-in-a-generation opportunity to put things right" and urged the Government to "create a genuinely independent system".
The letter states: "We are concerned that the current proposal put forward by the newspaper industry would lack independence and risks being an unstable model destined to fail, like previous initiatives over the past 60 years.
"No-one wants our media controlled by the Government but, to be credible, any new regulator must be independent of the press as well as from politicians."
Lord Black, chairman of the funding body for the Press Complaints Commission , told the Leveson Inquiry into media ethics that he wanted a form of "muscular" self-regulation.
That would mean a new organisation with the power to launch investigations and levy fines of up to £1m.
But signatories to the letter warned of fundamental weaknesses in the current system and called for a "credible" new regulator.
Lord Justice Leveson is expected to publish the findings of his inquiry in the next few weeks.
The investigation has heard evidence on phone hacking from celebrities and victims of crime as well as embarrassing revelations about the close relationship between some politicians and the media.
The letter adds: "After eight months, 650 witnesses and 6,000 pages of evidence submitted to the Leveson inquiry, we can be clear about two things.
"Firstly, that a free press is essential for a free society. Secondly, that there are fundamental weaknesses in the current model of self-regulation which cannot be ignored."
Brian Cathcart, director of campaign group Hacked Off, said: "This is a welcome development which shows that demands for a truly effective and independent system of regulation are coming from right across the political spectrum.
"The idea that the newspaper industry can get away with the shocking treatment of families like the Dowlers and carry on with business as usual is clearly nonsense.
"We hope the Prime Minister will seize the opportunity presented by his own backbenchers and agree to hold cross-party talks on how to take forward Lord Justice Leveson's recommendations as soon as it is practical to do so."