Prime Minister David Cameron has promised action to "get to the bottom" of the phone hacking scandal but said it was not just about the press but about the police and "about how politics works too".
Mr Cameron spoke out as as shockwaves from the scandal, which forced the closure of the 168-year-old News of the World, continued to reverberate.
His comments came shortly before his former communications chief and News of the World editor Andy Coulson was arrested over alleged phone hacking and illegal payments to police officers. The 43-year-old ex-editor of the News of the World was held at a south London police station on Friday morning, sources said.
Mr Cameron said a judge would be appointed to run an independent inquiry into how the scandal was allowed to happen, adding: "No stone will be left unturned."
Mr Cameron said a second inquiry would be held to examine the ethics and culture of the press and said that the Press Complaints Commission had failed, adding: "I believe we need a new system entirely".
Accepting some of the blame, Mr Cameron said party leaders "were so keen to win the support of newspapers we turned a blind eye to the need to sort this issue."
Amid demands from Labour leader Ed Miliband to apologise for hiring Mr Coulson, Mr Cameron said he took "full responsibility" for the decision but said others would judge whether it was the right decision to give him a second chance.
The Prime Minister said the bulk of the first inquiry, which would also cover other newspapers and the failure of the first Scotland Yard investigation into phone hacking, could not be carried out until after the new police probe was complete. But he said a second inquiry would begin immediately into the culture, ethics and practices of the British press.
He said: "Police investigations can only get you so far. What people really want to know is what happened and how it was allowed to happen. That is why the Deputy Prime Minister (Nick Clegg) and I have agreed it's right and proper to establish a full public inquiry to get to the bottom of what happened."
Mr Cameron also intensified pressure on News International chief executive Rebekah Brooks, who was editor of the News of the World at the time of Milly Dowler's phone being hacked. Referring to reports that she had offered her resignation, he said: "In this situation I would have taken it."