They have also announced plans to fast-track a new industry-led watchdog, which will be up and running just after Christmas.
The latest step in a bitter battle between politicians and the press in the wake of the phone hacking inquiry follows a decision by the Privy Council to reject industry plans for a new regulator created by a royal charter.
The Conservatives, Labour and the Liberal Democrats back plans for a rival Royal Charter, which the Queen could be asked to sign off on as soon as next week.
Opponents argue it could give politicians the power to meddle in the running of the press.
Lord Black of Brentwood, the chairman of the Press Standards Board of Finance (PressBof), said: "The decision by the Government and the Privy Council on this matter has enormous ramifications for free speech both here in the UK, and - because of our leadership role in the Commonwealth and developing world - across the globe.
"The Government and the Privy Council should have applied the most rigorous standards of consultation and examination of the Royal Charter proposed by the industry, which would have enshrined tough regulatory standards at the same time as protecting press freedom.
"They singularly failed to do so, and that is why - as the issues at stake are so extraordinarily high - we are having to take this course of action."
Last night campaign group Hacked Off criticised the move saying the newspaper industry was exposing itself as "desperate and deaf" and called on it to do what "the public expects of them".
Both Royal Charters would create panels to oversee independent regulators with the power to impose £1 million fines.
However, under the politician's plans changes could be made with the support of two-thirds of MPs, prompting fears of political interference.
Earlier this week the Queen was urged by a group of international press freedom bodies not to sign the politician's charter.
The creation of an independent regulator was the main recommendation of the Leveson report into press ethics, ordered by David Cameron in the wake of the phone hacking scandal.
Bob Satchwell, executive director of the Society of Editors said that the industry's plan would create the toughest regulatory system in the Western world.
He added that UK newspapers produce millions of stories a year "most of which raise no calls for complaint".
The Department for Culture, Media and Sport welcomed the progress the industry had made on establishing a new regulator but expressed disappointment it had decided to take legal action.