But the prime minister pointed out that Leveson had "emphatically" rejected allegations that the Conservative Party had struck some kind of deal with News International.
This related to claims that its newspapers might have offered favorable coverage to Cameron in the expectation of "policy favors."
Cameron's government faced uncomfortable questions earlier this year over its handling of a bid by Murdoch's News Corp. to take over British satellite broadcaster BSkyB. The bid was eventually dropped.
The prime minister also backed Lord Justice Leveson's recommendations to break an "excessively cozy relationship" between the police and the press.
Leveson said there was a perception that some senior police officers within London's Metropolitan Police were too close to News International.
But he found no evidence that decisions to limit its earlier inquiries into phone hacking were due to undue influence or corruption.
Leveson said senior police officers should ensure greater transparency over their meetings with the press in the future, and they should not be able to move immediately from the police into jobs in the media.
The Metropolitan Police said that the integrity of its officers had not been questioned but that it would study the criticisms made in the report.
Commissioner Bernard Hogan-Howe said he had already taken "decisive action" to address issues that emerged during the inquiry.
"Our priority now is the victims of phone hacking and making sure they get justice," he said.
Leveson described his inquiry, which heard from hundreds of witnesses during eight months of hearings, as "the most concentrated look at the press this country has ever seen."
Those testifying included politicians including Cameron and former Prime Ministers Tony Blair and Gordon Brown; police and media players such as Murdoch; and victims of press abuses.
The inquiry was first announced by Cameron in July 2011 in response to public outrage over a newspaper phone-hacking scandal.
The trigger was the allegation that in 2002, the voice mail of a missing 13-year-old girl, Milly Dowler, had been hacked by an investigator working for the News of the World newspaper before she was found murdered. Compounding the anger was the claim (later dismissed by police) that messages were deleted by him from the schoolgirl's full voice mail box, giving her parents false hope that she was alive.
The furor forced the closure of the 168-year-old News of the World, owned by News International.
It also prompted a new appetite among Britain's public and political establishments to see the sleazy underbelly of (often tabloid) reporting exposed and steps taken to clean up the media's act.
Leveson's report was the subject of much speculation before its release. Freedom of expression groups warned of a potential impacts on freedom of speech, while campaigners for greater controls said regulation is essential.
The chairman of the Press Complaints Commission, David Hunt, said he did not agree with all Leveson's recommendations but all those involved must seek to unite around "common ground."
"We all agree that we must regain the trust and confidence of the British people to make sure that unacceptable, outrageous and illegal behavior can never be allowed to happen again," Hunt said in a written statement.
The Committee to Protect Journalists issued a release saying it is "deeply concerned" about the recommendations.