their response to the Leveson report. Their response to how they're going to put in place a self-regulatory body that adheres to the Leveson principles and that is what I want to see moving forward swiftly."
Many of Friday's newspapers have praised Cameron's opposition to law-backed regulation.
But the father of Madeline McCann - the young girl who went missing in Portugal in 2007 - said he would have liked the report to have gone further.
"Although we broadly welcome Lord (Justice) Leveson's report, and it has many merits, for me, personally, I don't think the report has actually gone far enough," said Gerry McCann.
He said: "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".
McCann, who was the subject of what he called "unbelievably damaging" newspaper reports told BBC Radio 4's Today programme: "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. Without statutory underpinning, this system will not work".