A tougher form of self-regulation backed by legislation should be introduced to uphold press standards, the Leveson report has recommended.
Lord Justice Leveson said the press had "wreaked havoc in the lives of innocent people" for many decades.
But the report's recommendations have divided the coalition government.
David Cameron said he had "serious concerns" over statutory regulation but Nick Clegg said he supported some form of legal underpinning.
And Labour leader Ed Miliband urged the government to accept the report in its entirety.
Speaking in the Commons, Mr Cameron said he broadly welcomed Lord Justice Leveson's principles to change the current system.
But he said: "We should be wary of any legislation that has the potential to infringe free speech and the free press.
"The danger is that this would create a vehicle for politicians whether today or some time in the future to impose regulation and obligations on the press."
Deputy Leader Nick Clegg said changing the law was the only way to ensure "the new regulator isn't just independent for a few months or years, but is independent for good".
Mr Miliband described the report as "measured, reasonable and proportionate" and said Labour "unequivocally" endorsed its conclusions.
After the first of cross-party talks, a senior Labour source said Mr Cameron had agreed to ask the Department for Culture, Media and Sport (DCMS) to draft a bill to implement Lord Justice Leveson's recommendations.
The source added Labour would push for a Commons vote on implementing the recommendation in principle by the end of January.
The Hacked Off campaign, which represents victims of phone hacking said Mr Cameron's "failure" to accept the full recommendations of the report was "unfortunate and regrettable".
Founder Brian Cathcart said: "Despite their years of abuses and outrageous conduct, it seems that the prime minister still trusts the editors and proprietors to behave themselves. It seems that the prime minister wants self-regulation all over again."
Madeleine McCann's mother Kate said she hoped the report would "mark the start of a new era" for the press, in which it treated those in the news "with care and consideration".
Bob Satchwell, executive director of the Society of Editors said he hoped any British politician would hesitate before doing anything that "might in the slightest way threaten the freedom of the media".
"What happens 20 years down the line if you have a different government, which was upset by the press again, once you've given away the principle and put a law in place, it's very easy to amend."
Mr Cameron set up the Leveson Inquiry in July 2011 after it emerged journalists working for the Sunday tabloid the News of the World had hacked the mobile phone of murdered Surrey schoolgirl Milly Dowler. The paper was subsequently shut down by its owners News International.
Among Lord Justice Leveson's findings:
- All of the press served the country "very well for the vast majority of the time"
- The press must create a new and tough regulator backed by legislation to ensure it was effective
- This cannot be characterised as statutory regulation
- Legally-binding arbitration process needed to force newspapers to deal effectively with complaints
- Some "troubling evidence" in relation to the actions of some police officers - but no proof of widespread corruption
- Over last 30 years all political parties have had too close a relationship with the press which has not been in the public interest
- Former Culture Secretary Jeremy Hunt was not biased in his handling of News Corp's BSkyB bid but failed to supervise his special adviser properly
- The tabloid press often failed to show "consistent respect for the dignity and equality of women", and there is a "tendency to sexualise and demean" women.
In his 2,000-page report, Appeal Court judge Lord Justice Leveson said his proposals will protect the rights of victims and people bringing complaints.
He said the press had failed to properly regulate itself in the past, but he believed the law could be used to "validate" a new body.
He said: "There have been too many times when, chasing the story, parts of the press have acted as if its own code, which it wrote, simply did not exist.
"This has caused real hardship, and on occasion, wreaked havoc with the lives of innocent people whose rights and liberties have been disdained.
"This is not just the famous but ordinary members of the public, caught up in events (many of them truly tragic) far larger than they could cope with but made much, much worse by press behaviour that, at times, can only be described as outrageous."
Lord Justice Leveson said putting "a policeman in every newsroom is no sort of answer," because legal powers were limited to allow the press to act in the public interest.
However, the press is "still the industry marking its own homework", and needs an independent self-regulatory body to promote high standards, he added.
The Metropolitan Police said it accepted the criticisms made against it in the report.
Commissioner Bernard Hogan-Howe said he had already taken "decisive action" on the issues raised and his priority was now ensuring phone-hacking victims got justice.
The chairman of the Press Complaints Commission, Lord Hunt, said the press had to seize the baton and make sure it "doesn't let Lord Justice Leveson down".