Rupert Murdoch also appears to suggest in the recording, broadcast by Channel 4 News, that any journalists who were convicted and jailed in connection with the phone-hacking inquiry could get their jobs back. He is heard saying:
I will do everything in my power to give you total support, even if you're convicted and get six months or whatever.
You're all innocent until proven guilty. What you're asking is: what happens if some of you are proven guilty? What afterwards?
I'm not allowed to promise you - I will promise you continued health support - but your jobs. I've got to be careful what comes out - but, frankly, I won't say it, but just trust me.
A spokesman for News Corp told Channel 4 News: "Rupert Murdoch has shown understandable empathy with the staff and families affected and will assume they are innocent until and unless proven guilty."
The secret recording, broadcast this evening by Channel 4 News, hears Rupert Murdoch apparently railing at the the way the police behaved in arresting his journalists.
"Still, I mean, it's a disgrace. Here we are, two years later, and the cops are totally incompetent," he is heard saying, adding: "The idea that the cops then started coming after you, kick you out of bed, and your families, at six in the morning, is unbelievable."
He also is heard saying: "But why are the police behaving in this way? It's the biggest inquiry ever, over next to nothing."
Mr Murdoch is heard adding: "And now they're arresting their own, who never even took money... They're going to put all newspapers out of business."
Rupert Murdoch has been heard condemning police who are investigating alleged phone-hacking and illegal payments to officials by his journalists as "totally incompetent" in a secret recording broadcast by Channel 4 News.
The News Corp boss is heard apparently regretting the amount of information his company had handed over to the investigation - describing it as a "mistake" - while also appearing to tell staff who feared losing their jobs if found guilty of any offences to "trust" him.
The recording, obtained by the Exaro investigative website, was said to have been made in March during a meeting with journalists from The Sun at his newspapers' headquarters in Wapping, east London.
A spokesman for News Corp told Channel 4 News: "No other company has done as much to identify what went wrong, compensate the victims, and ensure the same mistakes do not happen again.
"The unprecedented co-operation granted by News Corp was agreed unanimously by senior management and the board, and (News Corp's management and standards committee) the MSC continues to co-operate under the supervision of the courts.
"Rupert Murdoch has shown understandable empathy with the staff and families affected and will assume they are innocent until and unless proven guilty."
Labour MP Siobhain McDonagh has given her reaction to accepting "very substantial" damages and a public apology from The Sun after her stolen mobile phone was accessed by the newspaper.
I'm in public life and I don't have a hang-up about my own privacy, but my family and constituents who had contacted me and given personal views were subjected to people seeing it. That made me feel very uneasy.
As an MP, people tell me all sorts of things, people give their personal information and they believe that you will do the right thing with it. That wasn't for anyone's eyes.
I was a government whip, I had lots of phone numbers and had then exposed all those people to having their privacy invaded, and that troubled me.
The Crown Prosecution Service (CPS) said it has droppws charges against a journalist investigated over phone hacking.
In a statement, the CPS said: "Having carefully considered the matter, the CPS has concluded that there is insufficient evidence for a realistic prospect of conviction in relation to that journalist."
Another journalist remains under investigation.
Former News of the World Deputy Editor Neil Wallis took to Twitter to say that he is the journalist who will not now face charges:
After 21 months of hell for my family, CPS have just told my solicitors that there will be NO prosecution of me re my phone-hacking arrest
A number of high profile phone-hacking cases are to be settled at the High Court today.
It is the latest in a series of case management conferences, ahead of a hearing in June.
At that time, compensation will be assessed in any outstanding claims for the second wave of the litigation.
Agreed statements of around 15 claimants could be read out to Mr Justice Vos today, with an estimated 160 claims on the register, and more coming forward.
Actress Sienna Miller was the first to publicly settle her privacy and harassment claim, for £100,000, in June 2011, with her ex Jude Law receiving the highest pay out so far, with compensation of £130,000.
The trial of a senior counter-terrorism detective accused of passing information to the News of the World is due to begin today.
Det Chief Insp April Casburn, 53, is accused of offering the now-defunct tabloid information about Operation Varec, the investigation into whether Scotland Yard's inquiry into phone hacking should be reopened.
She is due to appear at Southwark Crown Court today on one count of misconduct in public office, which she denies.
The trial is expected to take a week.
David Sherborne, who represents the core participant victims of phone hacking, said his clients welcome the findings and recommendations of the Leveson report.
He said the report included a "clear recognition of widespread failings in the culture, ethics and standard of the press and the devastating consequences this has had for the victims".
He said that the report calls for a regulatory system with "real teeth" and called on the current parliament to implement its recommendations.
Former News of the World editor Andy Coulson has won his appeal against a High Court ruling that News Group Newspapers (NGN) does not have to pay his legal costs arising from the phone-hacking affair.
Newspaper publisher Trinity Mirror is facing legal challenges over phone-hacking allegations for the first time, according to reports.
Former England football manager Sven-Goran Eriksson, former Beckham nanny Abbie Gibson, Coronation Street actress Shobna Gulati and ex-Blackburn Rovers captain Garry Flitcroft filed High Court claims alleging their voicemail messages were illegally accessed, the Financial Times (£) reported.
Their allegations relate to the Daily Mirror, the Sunday Mirror and The People newspapers, while Mr Eriksson's claim relates to the time Piers Morgan was editor of the Daily Mirror.
Mr Morgan has repeatedly denied claims he was involved in phone hacking, while Trinity Mirror told the FT, "We have no comment, we are unaware action has been taken at the High Court.”