Glasgow-born Gerry McCann said the Leveson recommendations for press regulation backed by the law is the "minimum acceptable compromise" for him and his wife Kate.
He warned that if the Government does not impose the regulations, his family will have relived their darkest days during the inquiry for no good reason.
The cardiologist claimed he and his wife "had the misfortune to suffer from everything the press could throw at us".
Mr McCann, whose three-year-old daughter vanished from a Portuguese holiday apartment in May 2007, said: "The reason we agreed to the ordeal of giving evidence to the Leveson Inquiry was that we don't want anyone else to have to go through what we went through. The Leveson package, including the legal underpinning, is the minimum acceptable compromise for us, and judging by the polls, for the public at large too. Leveson without the law is meaningless.
"When the Prime Minister promised to protect those who have been 'picked up and thrown to the wolves' by this process, we hoped for real change.
"The idea that Kate and myself, and the other victims, might have relived our darkest days in the full glare of the media, for no good reason, is offensive."
Mr McCann added that the country was at a crossroads, with the prospect of "lasting change to the failed system of press regulation".
"Our elected politicians face a critical choice," he added. "They can either do what Leveson recommends or they can turn their backs on the issue, and turn their backs on us, the victims of press abuse."
His comments came as campaign group Hacked Off claimed David Cameron has failed to give assurances that his proposals for press regulation will be "fully compliant" with Lord Justice Leveson's recommendations.
The Prime Minister met Hacked Off directors Brian Cathcart and Evan Harris ahead of this week's publication of the "Royal Charter", which will set out the Conservative party's plans in the wake of the Leveson Report. Mr Cameron has set his face against using statute to underpin regulation, arguing that it would "cross the Rubicon" after centuries of press freedom.
l Rupert Murdoch, the owner of The Sun, has hinted the newspaper's page 3 format of topless models may be nearing an end. He was responding to a tweet from a woman who said the page was "so last century!" He replied: "You maybe [sic] right, don't know but considering."