The News of the World's publishers have welcomed MPs' calls for a public inquiry into media industry standards following outrage at the phone hacking scandal.
Prime Minister David Cameron also supported holding one or more inquiries into the "absolutely disgusting" practice of illegally intercepting the voicemail messages of murder victims and their families.
"We do need to have an inquiry, possibly inquiries, into what has happened," Mr Cameron told MPs at Prime Minister's question time.
"We are no longer talking here about politicians and celebrities, we are talking about murder victims, potentially terrorist victims, having their phones hacked into.
"It is absolutely disgusting, what has taken place, and I think everyone in this House and indeed this country will be revolted by what they have heard and what they have seen on their television screens."
News International, the News of the World's publisher, said: "We also welcome today's cross-party calls for a broad public inquiry into standards and practices in the industry."
Mr Cameron said there were two "vital areas" that needed to be considered: why the original police inquiry failed to "get to the bottom of what happened", as well as the behaviour, practices and ethics of journalists and media organisations.
"Clearly, we can't start all that sort of inquiry immediately because you must not jeopardise the police investigation, but it may be possible to start some of that work earlier," he said.
He offered to hold talks on the matter with other party leaders, Attorney General Dominic Grieve and Cabinet Secretary Sir Gus O'Donnell.
Labour leader Ed Miliband said the police inquiry may take "some years" and insisted it was "possible to start the process now".