Guardian editor Alan Rusbridger said "a bit of statute" was a price worth paying for an effective new system of regulation and that he believed the press could "live with most of" the Leveson proposals.
"I think about 80% of it is right and can be agreed on," he told the BBC Radio 4 Today programme.
"It is right that is is open, that it is fair, that it's got sanctions, that it can investigate... that it's not picked from amongst the old cosy club.
"There are lots of things that are much better about the Leveson regulator than the one that existed before or the one that the press proposed."
A man who won libel damages after his arrest over the murder of a woman has written to MPs asking them to back Leveson's recommendations.
About 2,000 editors will sign up to a new independent press watchdog, the chairman of the Press Complaints Commission has said.
The Prime Minister has taken a political gamble by holding differing views to the victims, the Leveson inquiry and a majority of MPs.