Media playback is unsupported on your device Media caption Gerry McCann and Christopher Jefferies launch their national petition

Victims of press intrusion are urging the government to fully implement the Leveson Inquiry's recommendations on newspaper regulation.

Lord Justice Leveson called for a new independent watchdog - which he said should be underpinned by legislation.

Inquiry witnesses Gerry McCann and Christopher Jeffries launched the online petition, run by the campaign group Hacked Off.

Ministers say a draft bill on the report will be ready in a fortnight.

Lord Justice Leveson's 2,000-page report into press ethics, published on Thursday, found that some press behaviour had been "outrageous" and "wreaked havoc with the lives of innocent people".

He said the press - having failed to regulate itself in the past - must create a new and tough regulator but it had to be backed by legislation to ensure it was effective.

The report exposed divisions in the coalition government, with Prime Minister David Cameron opposing statutory control, unlike his deputy Nick Clegg, who wants a new law introduced without delay. Labour leader Ed Miliband also supports a new press law.

'Stand up for people'

Gerry McCann, whose daughter Madeleine went missing in Portugal in 2007, said he would have liked the report to have gone further.

Launching the petition he said: "Clearly the public want it, there's been a judicial review and I think the recommendations should be implemented. There's no good reason why they shouldn't be."

Analysis Government sources say they expect to produce a draft "Leveson" bill within a fortnight. However they expect the draft bill to underline their argument that any legislation would be much more unwieldy and extensive than envisaged by supporters of Leveson. They believe the draft bill will support their view that legislation would therefore be a threat to the freedom of the press. Instead, ministers want the newspaper industry to come forward with their own plans for regulation "within months." It's also being made clear that if the industry fails to agree on an acceptable revised package..then "the legislative stick remains an option." Earlier, Culture Secretary Maria Miller said alongside the issue of legislation, she had "very grave concerns" about some of the other details in the Leveson report -including on the role of Ofcom and rules on data protection. Labour sources say they fear the government will produce draft legislation that looks like "something the Stasi has written" in an effort to discredit the Leveson proposals

Mr McCann, who was the subject of what he called "unbelievably damaging" newspaper reports that suggested he and his wife killed Madeleine, added: "The press has been given enough chances, and in my opinion Lord [Justice] Leveson has given them another chance to put a structure in place which they are happy with."

Christopher Jeffries, who was wrongly arrested for the murder of Joanna Yeates, said: "Certainly I think it [Mr Cameron's decision] has been influenced by the pressure he has received from newspaper proprietors and editors and by some MPs in his own party."

Meanwhile, Hacked Off said victims had refused to meet Culture Secretary Maria Miller earlier because they felt "too let down" by the prime minister.

Following cross-party talks on Thursday night - which will resume next week - the Department for Culture, Media and Sport will begin the process of drawing up a draft bill implementing the Leveson recommendations.

The prime minister believes this process will only serve to highlight how difficult it is to try to legislate in a complex and controversial area while Labour and the Lib Dems think it will demonstrate the opposite.

Media playback is unsupported on your device Media caption Gerry McCann: Leveson does not go far enough

The Lib Dems pledged to ensure the legislation was drawn up "in good faith".

But the BBC's Norman Smith says Labour sources fear the Conservatives will produce draft legislation written in such a way as to discredit the proposals - "like something the Stasi [East German secret police] had written".

Culture Secretary Maria Miller told the BBC "the gauntlet has been thrown down" to newspapers to outline how they would set up tough self-regulation instead.

Proposed new press law Would: Create a process to "validate" the independence and effectiveness of the new self-regulation body

Validate a new process of independent arbitration for complainants - which would benefit both the public and publishers by providing speedy resolutions

Place a duty on government to protect the freedom of press Would not: Establish a body to regulate the press directly

Give any Parliament or government rights to interfere with what newspapers publish How new regulator might work

Mrs Miller said it was for the press to move forward "swiftly", putting in place a self-regulatory body that "adheres to the Leveson principles".

Government and industry sources have told the BBC that newspaper editors will meet Mrs Miller on Tuesday.

BBC political correspondent Ross Hawkins says she will tell them to draw up a better model for self-regulation than the one the press originally presented to the Leveson inquiry.

The Editors' Code of Practice Committee, which describes itself as the "foundation stone of the UK press self-regulatory system", said it would meet will meet next Wednesday to discuss the report.

Committee chairman Paul Dacre, editor of the Daily Mail, said: "We very much hope it will lay the framework for a fresh approach to the Editor's Code which will answer concerns raised during the inquiry."

Many of Friday's newspapers praised Mr Cameron's opposition to law-backed regulation.

But Guardian editor Alan Rusbridger told the BBC "a bit of statute" was a price worth paying for an effective new system of regulation and that he believed the press could "live with most of" the Leveson proposals.

Mr Rusbridger, who revealed that he spoke to other editors on Thursday night, said: "I think about 80% of it is right and can be agreed on."

Trevor Kavanagh, associate editor at the Sun, said there was no need for any new legislation.

"We welcome the report, its contents, its criticisms and we accept them. But I think that we've gone a long way as an industry to meeting also the recommendations for putting our house in order and making sure that it stays in order."