However, the newspapers could take legal action if the politicians' proposals -- which were drawn up without input from the newspaper groups -- are adopted and become a Royal Charter underpinning a new press regulation body.
The new system of arbitration proposes levying a fee on any party that wants to take action against newspapers.
In the wake of the Leveson Inquiry, which was sparked by revelations of phone hacking at the Rupert Murdoch-owned News of the World tabloid, newspapers proposed their own, alternative system of self-regulation.
He told the BBC: "They're either going to have to decide to live with it and work under this kind of Royal Charter or they're going to have to walk away from the process and say look, you, parliament, do what you like but we're going to set up our own regulator.
"We're not going play by your rules but we're going to get on with it and we believe that the version that we come up will satisfy what most people want."
The government proposals foresee the creation of an "independent, self-regulatory" body which would have the power to fine newspapers up to 1 million pounds (USD 1.6 million, 1.2 million euros).
Bob Satchwell, executive director of the Society of Editors, said the press would never accept the politicians' proposals.
"You can't expect anybody to take on board something which is put upon them by politicians," he told BBC television.
"The differences (between the sides) now, after all this time, are actually very small but they're very important.
"You can't have a half-free press. It's got to be free or not.
