"A media regulatory body anchored by statute cannot be described as voluntary," the committee's executive director, Joel Simon, said in the release. "Moreover, adopting statutory regulation would undermine press freedom in the UK and give legitimacy to governments around the world that routinely silence journalists through such controls."
Index on Censorship, a free speech group, urged "serious, considered debate" about the points made by Leveson.
Chief executive Kirsty Hughes said: "We share David Cameron's concerns that statutory underpinning would undermine free speech, and could be the start of a slippery slope of government interference in the media."
Media reform campaign group Hacked Off launched an online petition that calls on the leaders of the three main parties to implement the Leveson Report's recommendations in full "as soon as possible."
The actions of staffers at News Corp. and News International came under close scrutiny during the inquiry.
Among those to testify were Murdoch protege Rebekah Brooks, former chief executive of News International and onetime editor of the Sun and News of the World, and Andy Coulson, who also edited the News of the World. He went on to become Cameron's director of communications before resigning from that post early last year.
Both appeared in court Thursday morning to face charges of conspiracy to commit misconduct in a public office in connection with alleged illegal payments to public officials. They and three other accused were released on bail and ordered to appear in court again next week.
The scandal has also raised the specter of possible legal action against News Corp. staffers in the United States under the Foreign Corrupt Practices Act, which outlaws the bribery of foreign officials by U.S. firms.
However, analyst Porter Bibb in New York said the release of the Leveson report is "a nonevent" from the point of view of U.S. investors and would have no real impact on News Corp. stocks.
The corporation is doing well and Murdoch has come back "stronger than ever" following the pressure he was under to cede control of parts of his media empire early this year, Bibb said.