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As MPs debate the Leveson report in parliament, more than 130,000 people have signed a petition by the campaign group Hacked Off to call for the implementation of the inquiry's recommendations.
The Culture Secretary has issued a warning to the newspaper industry in the wake of the Leveson report saying that "if the industry doesn't respond then the government will".
Speaking to the House of Commons, Maria Miller said that maintaining the status quo was not an option for the industry and that the report had highlighted the scale and breath of abuse conducted by the press over the past few years.
Lord Justice Leveson and Prime Minister David Cameron have been called to give evidence to a parliamentary committee report on press regulation, it has emerged.
The House of Commons Culture, Media and Sports Committee has launched a new inquiry into press regulation. It is hoped that the Appeal Court judge - who published his report on the issue last week - and the PM will be witnesses.
At a private meeting of the committee last week, it was agreed that invitations would be sent to Mr Cameron, Lord Justice Leveson, and the Press Complaints Commission chairman Lord Hunt. Guardian editor Alan Rusbridger and representatives of the Hacked Off campaign have also been invited.
John Tulloch, whose phone was hacked after he survived the 7/7 London bombings, has told Daybreak that there are "a large number of people calling for the regulation of the press."
He said: "Lord Leveson, a large amount of the public, the leaders of two parties and a large number of victims of the media [are calling for it]. That's quite a big argument."
Cross-party talks on the Leveson report will resume today in a bid to find a solution to press regulation that meets the requirements set out in the report. Daybreak's Sue Jameson reports.
Cross-party talks on the Leveson report will resume today in a bid to find a solution to press regulation that meets the requirements set out in the report.
On Sunday, a Labour Party source said it was committed to cross-party talks on the report.
However, they warned that it had begun drafting its own Bill based on Lord Justice Leveson's recommendations for regulation of the press and will use it as the basis for a Commons vote if the Prime Minister blocks reform.
Campaign group Hacked Off have projected an image on to Parliament urging people to sign up to their online petition calling for the Leveson recommendations to be implemented in full
The petition has attracted more than 123,000 signatures since it was launched on Friday.
The Labour Party has begun drafting its own Bill based on Lord Justice Leveson's recommendations for regulation of the press and will use it as the basis for a Commons vote if the Prime Minister blocks reform, a source said.
Labour is frustrated by suggestions that draft legislation David Cameron ordered to be drawn up was simply an exercise in showing the plans are unworkable.
The party has brought in a team of legal experts to put together proposals within two weeks that would implement the core principles of the Leveson Report's findings.
The Labour source said the party was committed to cross-party talks on the report, which resume tomorrow between culture Secretary Maria Miller and her opposite number Harriet Harman.
But they warned, "If they [the talks] are not successful, Ed Miliband does want to push this to a vote".
Latest ITV News reports
A man who won libel damages after his arrest over the murder of a woman has written to MPs asking them to back Leveson's recommendations.
About 2,000 editors will sign up to a new independent press watchdog, the chairman of the Press Complaints Commission has said.