Madeleine McCann's mother Kate says she hopes the Leveson report will mark the start of a new era for the press and has urged David Cameron to "embrace the report and act swiftly".
Mrs McCann gave moving evidence to the Leveson Inquiry about the intense media interest after her daughter went missing during a family holiday in Portugal in 2007 and was at the Queen Elizabeth II conference centre for the report's publication.
She said: "I welcome Lord Leveson's report and hope it will mark the start of a new era for our press in which it treats those in the news responsibly, with care and consideration.
"I hope the Prime Minister and all the party leaders will embrace the report and act swiftly to ensure activation of Lord Leveson's recommendations within an acceptable and clearly defined timescale."
The Prime Minister told the Commons he has "serious concerns and misgivings" about bringing in laws to back a new system of press regulation.
His statement has angered victims of press intrusion, who have demanded the independent, self-regulatory body underpinned by legislation proposed by Lord Justice Leveson has "real teeth".
But senior figures from News International and the Telegraph Media Group have said newspapers will resist any legislation backing up a new regulator.
Actor Hugh Grant said intrusion victims felt "betrayal" when they heard David Cameron's response to Lord Justice Leveson's report.
The Love Actually star, who has backed the Hacked Off campaign group, tweeted: "With a group of (non celeb) victims including Hillsborough families listening to PM. Buzzword is betrayal."
Former Crimewatch presenter and hacking victim Jacqui Hames told a press conference she found Mr Cameron's statement "rather depressing".
She said the PM's support of the majority of the report was "good" but added: "It starts to fall apart without the underpinning regulation."
Earlier she said Lord Leveson had "rightly condemned this outrageous conduct of the press in recent years" and called for a deadline for newspapers to join the proposed new self-regulatory body.
Hacking victim Graham Foulkes, whose son David was killed in the 7/7 London bombings, welcomed the report but said he would not support legislation.
He also criticised the "hijack" of the Leveson inquiry by celebrities with an "agenda".
He told Sky News: "My concern is the notion that parliament are going to become involved in regulating or licensing or have got a toe in the door of having control over the media.
He added: "For the first time that I can remember an inquiry was set up for ordinary people and it set off with the right motivations... but very quickly the Hugh Grant roadshow came to town, the celebrity circus, and it became OK magazine overnight."
"I didn't feel it ever quite got back on track, but I've been proved wrong today because Sir Brian (Lord Leveson) has pulled it out of the bag."
The man wrongly arrested for the murder of Joanna Yeates has said it would be a "disaster" if Mr Cameron failed to implement the Leveson proposals in full.
Her landlord, retired teacher Christopher Jefferies, 67, told ITV News he would feel "let down" if the Prime Minister decided to side-step recommendations on legislation.
"I would certainly feel let down," he said. "I would think it would be a disaster."
Former Formula One boss Max Mosley said it would be "astonishing" if the Government did not implement Lord Leveson's recommendations.
Mr Mosley won £60,000 in damages from News Of The World in 2008 over an article alleging that he took part in a "sick Nazi orgy", which he denied.
He told Sky News: "It certainly is a very thorough document and it's in many respects better than one could have hoped.
"The only real omission is that if you want to stop something coming out because you find that they are going to breach your privacy, you would still have to go to court to do that, which of course is very expensive.
"I think it would be astonishing if the politicians didn't implement the report because no responsible politician could allow the current situation to continue," he added.
Many in the media were supportive of Mr Cameron's reluctance to rush down the statutory regulation route.
Carl Bernstein, one of the investigative journalists who broke the Watergate scandal in the US, 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."
News International chief executive officer Tom Mockridge said the former publisher of the News Of The World backed Mr Cameron's "rejection" of new legislation.
He 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.
"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."
Lord Black of Brentwood, the chairman of the Press Standards Board of Finance and executive director of the Telegraph Media Group warned that aspects of the proposals are "profoundly dangerous" and would put a state regulator "at the very heart of the newsroom".
Lord Hunt, head of the widely discredited Press Complaints Commission (PCC), said: "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 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."
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."
Following criticism of relationships between police and journalists during the Leveson Inquiry, Andy Trotter from the Association of Chief Police Officers said forces would "build upon" measures already taken to tighten up guidance.
He said: "Police should have a professional, open and transparent relationship with the public and the media. The media can provide a vital role in communicating with the public, helping society to solve crime, and holding public institutions to account."