Maria Miller, the Culture and Media Secretary, said a sub-committee of the Privy Council found the newspaper industry's plans had failed to comply with some important principles in the Leveson report on press regulation, including independence and access to arbitration.
In a Commons statement, she said the Coalition was willing to consider some of the industry's ideas and would seek to improve its proposals for a royal charter to underpin regulation.
During the next 72 hours the minister will hold talks with Labour and LibDem colleagues to secure agreement for an amended charter to be published on Friday and approved by the Privy Council on October 30.
Ms Miller said: "We have a once-in-a-generation opportunity to get this right. We all want it to be the best we can do to give individuals access to redress whilst safeguarding this country's free press which forms such a vital part of our democracy."
However, Harriet Harman, Labour's deputy leader, called for the Privy Council to decide matters when it meets later today, saying: "There has been nearly a year since Leveson reported and six months since this House agreed the draft charter. There has already been too much delay. Let's have no further delay, let's get on and implement Leveson."
John Whittingdale, the Conservative chairman of the Commons Culture Committee, warned it would be infinitely preferable to establish a system which as many newspapers as possible were ready to sign up to.
During Commons exchanges, Ms Miller made clear any changes to the Government proposals were unlikely to be fundamental but rather would touch on issues such as the addition of a clause that would implement the cross-party charter in Scotland.
She also suggested there could be concessions on a new arbitration unit, which local papers have said could trigger a new industry of "ambulance-chasing" lawyers looking for cash compensation from titles already struggling for survival.
However, Labour's Chris Bryant said events felt like "Groundhog Day", saying: "Surely to goodness it's time we listened to the public ... if you default on this timetable, surely this House should take the matter into its own hands?"
The Secretary of State replied: "I'm sure you wouldn't really be implying you did not want us to make the improvements we have made with regard to Scotland? Or indeed, perhaps, you are implying we should ignore the very real concerns of local press about the costs of arbitration? You might want to ignore local press but I don't want to."
Brian Cathcart, director of pressure group Hacked Off, which includes actor Hugh Grant, said it was time publishers "accepted a workable, fair solution that poses no threat whatsoever to freedom of expression in this country".
However, the industry said it was disappointed and warned it was impossible to see how the Government's charter could comply with Leveson's recommendations, which envisaged "a body, established and organised by the industry which would provide genuinely independent and effective regulation of its members".
It was suggested there were fears within the Coalition that newspapers might launch a legal challenge to the Privy Council's decision and that if the Press took the matter on in a confrontational way then the Queen, who cannot be seen to be engaged in any political arguments, might refuse to formally sign the royal charter.