The letter from 42 MPs and two peers, including four ex-cabinet ministers, opposed newspapers' continued preference for self-regulation in the post-Leveson media world.
Published by The Guardian, the letter has been signed by Lord Fowler, Sir Malcolm Rifkind, Caroline Spelman, George Eustice, Zac Goldsmith, Nicholas Soames and others.
While backing a free press, the letter adds: "There are fundamental weaknesses in the current model of self-regulation which cannot be ignored.
"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.
"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."
The letter called for the creation of a "genuinely independent system" of regulation, while agreeing with Prime Minister David Cameron that "obsessive argument about the principle of statutory regulation can cloud the debate".
It noted that state regulation in law and broadcasting has not compromised the independence of the legal profession or of TV channels.
The signatories described the Leveson Inquiry as a "a once-in-a-generation opportunity to put things right" and called on parliament not to "duck" the challenge it presents.
"The worst excesses of the press have stemmed from the fact that the public interest defence has been too elastic and, all too often, has meant whatever editors wanted it to mean," the letter continued.
"To protect both robust journalism and the public, it is now essential to establish a single standard for assessing the public interest test which can be applied independently and consistently."
A source added to the newspaper: "As Conservatives, we are reluctant regulators and we firmly believe in a free press, and want to help newspapers survive, but they have to meet us half way.
"Their refusal to countenance any kind of statutory change to raise standards is no longer acceptable to the Conservative party.""