Politicians, campaigners and media executives are divided over Lord Justice Leveson's recommendations for reform of the press.
Campaign group Hacked Off, which has represented some of those complaining of unwarranted press intrusion, said proposals for regulation supported by legislation were "proportionate" and called for them to be implemented quickly.
But industry figures and civil liberties campaigners warned against backing up any new regulatory body in law.
Lord Hunt, head of the Press Complaints Commission, said: "Above all it is absolutely key that the result is a new regulator with effective sanctions and teeth, and independent from the industry and from the Government. I have to say, however, that I am not convinced statutory regulation including supervision of press regulation by Ofcom would have prevented the horrors of the past. What will prevent them happening again is getting the press to sign up to a fresh start and a serious improvement in governance and culture."
Tom Mockridge, News International chief executive officer, said: "As a company we are keen to play our full part, with others in our industry, in creating a new body that commands the confidence of the public. We believe that this can be achieved without statutory regulation - and welcome the Prime Minister's rejection of that proposal.
"We accept that a new system should be independent, have a standards code, a means of resolving disputes, the power to demand prominent apologies and the ability to levy heavy fines."
Former Formula 1 boss Max Mosley, who successfully sued the News of the World for privacy damages over claims that he was involved in a "sick Nazi orgy", said it would be "astonishing" if the Government did not implement Lord Justice Leveson's recommendations.
Nick Pickles, director of civil liberties campaign group Big Brother Watch, said: "If Parliament votes on the press, the press isn't free. To split hairs between statutory underpinning and statutory regulation is not an acceptable distinction in a free and democratic country."
Bob Satchwell, executive director of the Society of Editors, warned that detailed statutory underpinning of regulation could be dangerous. He told Sky News: "What you can't have is too much detail in any kind of statutory underpinning, that's where the danger lies. Most politicians, once you give them a little nose into something, will try to find a very much wider thing down the line. We might have benign politicians now, but 10 years' time? That's the problem."
Carl Bernstein, one of the investigative journalists who broke the Watergate scandal, said the British press was right to resist legislation. He told Channel 4 News there were already enough laws in the UK to put journalists who hacked phones in jail. "The answer is find the proper way to put them in jail for the horrible offences that they are guilty of, not to try and restrain free speech, freedom of the press - that is going to come back and bite British democracy in the ass because that is what this is about. It's an easy answer to a tough problem."