David Cameron has said press regulation plans proposed by the industry have "serious shortcomings" as he defended the delay in pushing through the version backed by MPs.
Following cross-party talks, Cameron, Ed Miliband and Nick Clegg agreed a compromise that would see a new system of regulation overseen by a royal charter.
However newspapers are still unhappy with the plan and have published their own rival charter.
Last week the government was forced to admit it implementation of a new system of press regulation has been delayed in part because ministers were too slow in submitting their royal charter to the privy council. The council can only consider one royal charter at a time, and the newspaper industry managed to submit its version first.
Victims of press intrusion, including the parents of missing girl Madeleine McCann and Harry Potter author JK Rowling, today wrote an open letter to culture secretary Maria Miller
"We are aware of calls for further delay," they wrote. "We urge you to recall that the March 18 Charter has the backing of Parliament, is founded on the recommendations of a duly constituted public inquiry that painstakingly took account of the views of all stakeholders, and is supported by the great majority of victims of press abuses.
"It would be appalling if such people, in defiance of the will of the rest of society, were allowed to delay the implementation of a Government policy that has been formally approved by parliament."
On Tuesday it was also reported that Lord Justice Leveson has agreed to be subjected to a grilling by MPs over his proposals for the future regulation of the press.
The judge, whose report prompted a fierce backlash from many newspapers as well as some MPs who feared the recommendations threatened the freedom of the press, is said to have made himself available to appear on 24th July.
However the culture committee had wanted Leveson to give evidence before the summer recess - which begins on 18 July.
John Whittingdale, the chairman of the committee, told The Huffington Post UK in June that MPs were keen to hear Leveson's views on the stalemate.
Whittingdale said that as the two royal charters proposed were not part of Leveson's initial report, the committee wanted to establish if the judge felt either "delivers the kind of system" he would be happy with.
The veteran Tory MP also said the fact Leveson was a judge should not prevent him from appearing before a parliamentary committee.
"He chaired an inquiry which made recommendations to parliament, it doesn't seem unreasonable that parliament ask him some questions about that," he said. "If he were sitting a judge delivering a verdict on a case that would be different. That wasn't the case in this instance, he was the chairman of public inquiry."