Plans for a new press regulator backed by a Royal Charter are "a compromise of a compromise" that do not go far enough in holding the press to account, the parents of missing girl Madeleine McCann have warned.
Gerry and Kate McCann hit out at the Government's proposals, saying they lacked transparency and gave newspapers a last chance at self-regulation they did not deserve.
The main political parties appeared last week to be nearing agreement on plans for a Royal Charter that would oversee a new press watchdog.
Labour and the Liberal Democrats gave a cautious welcome to Tory proposals for creating a body to verify a new regulator set up by the industry.
Mr McCann told the BBC's Andrew Marr Show: "I think Leveson has been quite generous to the press and more than the behaviour of some sections of the media deserve really.
"They are getting a last chance at self-regulation which for me was actually a step too far."
He added: "I feel that the press has lost its entitlement to self-regulation over many, many years and I would have liked to have seen statutory regulation, not self-regulation."
Madeleine was nearly four when she vanished from her family's holiday apartment in Praia da Luz in the Algarve on 3 May 2007, where she had been left by her parents as they dined at a tapas restaurant with friends nearby.
The coverage of her disappearance was given by Lord Justice Leveson as an example of how stories ran "totally out of control".
Giving evidence to the inquiry last year, Kate McCann said she felt like "climbing into a hole and not coming out" after the News of the World printed her intensely personal diary, started after her daughter disappeared.
They also criticised other papers' coverage of her disappearance.
Earlier, John Witherow, the acting editor of The Times and former long-serving editor of The Sunday Times, told Marr presenter Eddie Mair that what was being proposed in the Royal Charter "had teeth" and took in much of Leveson but without the need for statute.
"What is on the table is very tough on the press," he said, adding that "we don't like parts of it", especially around damages payouts.
Speaking on Marr, Mrs McCann said: "What the Government is proposing with this Charter – the charter body is overseen by ministers for a start which again takes away the independence – it is basically a compromise of a compromise.
"Why do the press, the Government, not want to be accountable like everybody else? The press are the first to hold people in authority to account."
The McCanns still hold out hope their daughter is alive and complained that stories were still appearing which they believed compromised her safety.
"We still have episodes where things are published which we would much prefer were not published," McCann said.
"It is something we raised at Leveson that Madeleine and her safety is often treated with complete contempt and we have no redress currently."
Bob Satchwell, executive director of the Society of Editors, said: "They (the McCanns) are wrong to think that the tough new self regulatory regime requires a statute.
"No-one, including politicians of all parties, really wants to see that with the inherent long terms dangers, so long as another form of guarantee about the independence of the system is put in place."
He added that Lord Justice Leveson recognised that the "vast majority" of journalists were "blameless", adding: "There are complex practical and legal issues in implementing the new system, but the Leveson pathway will be closely followed.
"That is what the Royal Charter plan is trying to achieve so that the principles of the new system agreed more than a year ago by the industry, even before Lord Justice Leveson reported, can be implemented quickly, hopefully by the middle of this year.
"The Leveson principles are not being undermined and the provisions of the strict new system, with fines of up to £1 million, demonstrate that the press has not been let off any hooks."