Editors will agree to a stronger code of conduct without the need for statutory legislation, David Hunt, the chairman of the soon-to-be-scrapped Press Complaints Commission has told Sky News.
Lord Justice Leveson was wrong to say such a move was needed to persuade editors to join a new system, Lord Hunt said.
"He doesn't think they will sign; I do. I have spoken to 120 publishers speaking on behalf of 2,000 editors. They have all told me they will sign up," he said on the Murnaghan show.
He wanted five-year rolling contracts to ensure publications could not "walk away" from a new regime, he added.
Earlier, a key aide to Lord Justice Leveson claimed the press reform laws he had called for would be illegal and might breach the Human Rights Act.
Shami Chakrabarti, one of six advisers who worked with the judge on the inquiry, told the Mail On Sunday she could not support legislation because it would "coerce" newspapers into holding higher standards than anyone else, which would be unlawful.
Ms Chakrabarti,the director of civil rights group Liberty , warned that Lord Justice Leveson's proposal for an independent regulatory body backed up in law could have "serious unintended consequences".
"In a democracy, regulation of the press and imposing standards on it must be voluntary. A compulsory statute to regulate media ethics in the way the report suggests would violate the Act, and I cannot support it," she said.
In contrast, actor and Hacked Off member Hugh Grant, said the findings of the report should be implemented, arguing that Lord Justice Leveson's recommendations were "mild" and said Mr Cameron's position was "very close to disgraceful".
"We thought the report was intelligent and clever but at the mild end of what everyone hoped for," Grant told the BBC's Andrew Marr Show.
"We thought the upside of it being mild was that there was no way the Prime Minister can't endorse this, this is something that can get through."
He spoke of his "astonishment" at Mr Cameron's "betrayal" by declaring there was no need for statutory underpinning. Reforms "simply won't work without it", he said.
David Cameron has said he has "serious concerns and misgivings" about legislative action, but the PM is facing continuing pressure from victims of press intrusion, the public and other party leaders to implement the findings.
More than 100,000 members of the public have signed a petition organised by Hacked Off , calling for the recommendations to be implemented in full.