Leveson said over the past three decades, political parties "have had or developed too close a relationship with the press in a way which has not been in the public interest."
He acquitted senior politicians of wrongdoing, but recommended that political parties publish statements "setting out, for the public, an explanation of the approach they propose to take as a matter of party policy in conducting relationships with the press."
Parliament will have to approve the legal changes the report recommends, and Cameron is under intense pressure from both sides. He is also tainted by his own ties to prominent figures in the scandal.
Former Murdoch editors and journalists charged with phone hacking, police bribery or other wrongdoing include Cameron's former spokesman, Andy Coulson, and ex-News of the World editor Rebekah Brooks, a friend of the prime minister.
Coulson and Brooks were appearing in court Thursday on charges of paying public officials for information.
Cameron, who received a copy of Leveson's report a day early, is due to make a statement about it in the House of Commons later Thursday.
He and other senior politicians insist they will not curb Britain's long tradition of free speech.
"Everybody wants two things: firstly, a strong, independent, raucous press who can hold people in positions of power to account, and secondly to protect ordinary people, the vulnerable, the innocent when the press overstep the mark," Deputy Prime Minister Nick Clegg said Thursday.
"That's the balance that we are trying to strike and I am sure we will."
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