The cross-party proposals for the 'Royal Charter' to underpin greater self regulation among the country's media outlets had been opposed by a number of major newspaper bosses as a threat to press freedom.
A spokesperson of Prime Minister David Cameron's office has now said it "made sense" for both versions to be considered at the same time.
The government's charter was due to be presented to the Queen on May 15 by the Lord President of the Privy Council, Deputy Prime Minister Nick Clegg.
The inquiry had found that the existing Press Complaints Commission was not sufficient for the regulatory task and that a new independent body with legal sanctions was required.
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However, the newspaper industry presented its own plan of a rigorous system of regulation, which kept the press free from state interference.
According to this proposed system, fines of up to 1 million pounds can be imposed, along with giving readers the chance to have their say over how journalists should behave.
The Hacked Off group, which is fronted by the actor Hugh Grant and campaigns for tighter press regulation, said: "Press reform has been overdue for decades. If there is another delay for a further month, that can be borne."
The Guardian and the Independent are the only two national newspaper titles, out of 11, that have not signed up to the alternative proposal, which has received the support of some politicians like London Mayor Boris Johnson and Commons culture committee chairman John Whittingdale too.