Responding to the report Prime Minister David Cameron said he supported many of the recommendations and points made by Lord Justice Leveson, adding that he accepts the principles of an independent self-regulatory body.
However he had "some serious concerns and misgivings" on the recommendation for statutory underpinning of the regulation.
"On the grounds of practicality, no matter how simple the intention of the new law, the legislation required to underpin the regulatory body would, I believe, become more complicated," he added.
Following publication of the report a number of groups have also issued statements responding to some of the key recommendations. Here are just some of the statements which have been issued so far.
Lord Hunt, PCC
"Sir Brian Leveson is to be congratulated on a massive piece of work. Although I do not agree with all of the conclusions, I must praise him and his dedication and commitment.
"We all agree that we must regain the trust and confidence of the British people to make sure that unacceptable, outrageous and illegal behaviour can never be allowed to happen again.
"So we now need to find a way forward. I suggest that we all now digest this report and seek our common ground and then unite around it. 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 suggest that we all now digest this report and seek our common ground and then unite around itLord Hunt, PCC
"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."
The Media Standards Trust
The Media Standards Trust says it "welcomes Lord Justice Leveson’s sensible and pragmatic report".
Director Martin Moore said: "Lord Justice Leveson has called the press's bluff and challenged them to go back to the drawing board and come up with a genuinely independent plan for self regulation."
And acting chair Baroness Helena Kennedy added: "No-one can complain that this limits freedom of expression. The real question is can the press finally make itself properly accountable."
Financial Times editorial
"The Financial Times has reservations about this approach. While there may be merit in a grand bargain that trades the incentives to participate for some measure of statutory underpinning, the idea of handing oversight power to Ofcom is wrong-headed.
"Ofcom is charged with regulating television broadcasters that have a legal obligation to impartiality. It reports directly to government. This is a step down the road towards state licensing of a press that, of course, has no obligation to provide balance.
"This newspaper is also worried about Lord Justice Leveson’s proposals for a 'backstop regulator' that would step in if news organisations did not join the new body. This explodes the concept of voluntarism that lies at the centre of his recommendations. It is a press law by the back door and one that pays scant attention to the revolutionary changes in the media landscape. This is increasingly dominated by digital innovators and social media.This newspaper is also worried about Lord Justice Leveson’s proposals for a 'backstop regulator' that would step in if news organisations did not join the new body. This explodes the concept of voluntarism that lies at the centre of his recommendationsFinancial Times editorial
"The newspaper industry must now respond constructively. It has been given time to develop reforms that are workable and command public trust. Whatever its recent failings, the press remains a cornerstone of our democracy. This should not be forgotten."
Tom Mockridge, chief executive, News International
"We are grateful to Lord Justice Leveson for his thorough and comprehensive report, and will be studying its recommendations and comments in detail.
"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.
"We have spent 18 months reflecting upon these issues and are determined to move on as soon as possible with others in our sector to set up a new body that will ensure British journalism is both responsible and robust."
National Union of Journalists
In a statement the NUJ said it was particularly pleased by the recommendation by Leveson of a conscience clause in journalists' contracts.
General secretary Michelle Stanistreet said: "From the outset of the Leveson inquiry, we demanded a conscience clause to safeguard journalists who object to being made to act unethically in the pursuit of a story.
"The NUJ has been campaigning for years for a conscience clause in contracts of employment and we are delighted that Lord Justice Leveson has listened to the voice of journalists.
"The NUJ will now do all it can to ensure that when journalists stand up for a principle of journalistic ethics they have a contractual protection against being dismissed."The NUJ has been campaigning for years for a conscience clause in contracts of employment and we are delighted that Lord Justice Leveson has listened to the voice of journalistsMichelle Stanistreet, NUJ
She added: "The NUJ welcomes Lord Justice Leveson's support for a free press and independent regulation of the press – independent of both government and of the industry.
"We're also pleased that the recommendations include civic society involvement and the recommendation that the new body needs an independent chair and board appointed in a fair and transparent process. The board should include the voice of journalists, through the NUJ."
However she added "it is disappointing that Lord Leveson has not made recommendations in relation to media ownership and plurality – it is significant that the unfolding scandal at News International happened in a company with a 35.15 per cent share of the market and in a workplace where the NUJ has been effectively blocked by Rupert Murdoch for years.
"The NUJ will now look at the details of the report."
"English PEN welcomes Lord Justice Leveson's recognition of the fundamental role played by the press in society, not only in the public interest but in educating and entertaining.
"We are reassured by his acknowledgement of the importance of regulation that is independent of government, politicians and industry and by his proposal for there to be a positive duty on the government to protect the freedom of the press.
"We are also delighted that he has supported English PEN and Index on Censorship's proposals for swift, low cost dispute resolution, which forms an integral part of the recommendations.
"However we have serious concerns about the incentives that are at the heart of his proposals, which are underpinned by legislation."
Index on Censorship
"Index urges that there is a serious, considered debate about Lord Justice Leveson’s recommendations. The free speech organisation opposes the statutory underpinning of press regulation proposed by Lord Justice Leveson."We consider that the statutory-voluntary approach to independent press regulation would undermine press freedom in the UKIndex on Censorship
Chief executive Kirsty Hughes added: "We consider that the statutory-voluntary approach to independent press regulation would undermine press freedom in the UK. However, we support the proposal for cheap, effective arbitration, which would help victims get swift redress to their complaints."
President of the Newspaper Society Adrian Jeakings said: "The UK’s local media had nothing to do with the phone-hacking scandal which prompted the Leveson inquiry but we have been all too aware that hundreds of responsible regional and local newspapers would inevitably be caught up in any resulting new system of press regulation.
"We therefore welcome the Leveson report's praise for the important social and democratic role played by the local press, his acknowledgement that the criticisms of the culture, practices and ethics of the press raised in this inquiry were not directed at local newspapers and his recommendation that the regulatory model he proposes should not provide an added burden to our sector.
"However, local newspapers have always been vehemently opposed to any form of statutory involvement or underpinning in the regulation of the press, including the oversight by Ofcom proposed in the report. This would impose an unacceptable regulatory burden on the industry, potentially inhibiting freedom of speech and the freedom to publish.
"We believe the industry is in a position to establish the sort of tough new system of independent, accountable press regulation with the power to investigate wrongdoing and levy fines, envisaged by the report. All major news publishers – and some internet news providers – have indicated they will join such a system provided there is no statutory backstop. In practice, this independent self-regulatory system would almost certainly be stronger and more effective than any statutory model could ever be and could be put into place very quickly.
"Newspapers are ultimately accountable to their readers and must abide by the laws of the land. But, as the prime minister has today acknowledged, a free press cannot be free if it is dependent on and accountable to a regulatory body recognised by the state."