The father of missing Madeleine McCann said legal backing for any new system was the "minimum acceptable compromise for me and for many other victims" and urged the Prime Minister to "do the right thing".
He told the BBC Radio 4 Today programme: "I would have liked to have seen a properly independent regulation of the press, whereas I think he has given the press another opportunity of self-regulation."
It should be made compulsory and measures put in place make journalists more accountable, he said.
He added: "But I do accept that full implementation of Lord (Justice) Leveson's report is the minimum acceptable compromise for me and I think for many other victims who have suffered at the hands of the press.
"The Prime Minister and our other elected politicians have an opportunity now to do the right thing. And if they do the right thing, for the public, then it will help restore a little confidence.
"I clearly respect his opinion but I personally disagree with the viewpoint and Lord (Justice) Leveson, as a senior law judge of our country, has made clear that what he is proposing is not a state-run press.
"It is a fine distinction but without the statutory underpinning this system will not work."
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The toddler died after suffering eight months of abuse at the hands of her legal guardian Kandyce Downer.
After a cool start, Thursday will be another dry and warm day with some good spells of sunshine.
A cool start to Thursday. A dry and sunny day should develop, with plenty of warm sunshine as winds also remain light.