In one clip from a secret audio recording obtained by Channel 4 News, Rupert Murdoch is heard branding police "totally incompetent" and damning the Scotland Yard inquiry into corrupt payments to public officials.
"It's the biggest inquiry ever, over next to nothing," he says.
Hear more of the recordings at Channel 4 News.
A News Corp statement said Mr Murdoch was showing "understandable empathy" to his staff.
Defending Rupert Murdoch's pledge to staff, 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 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.
An MP has called for police action after Rupert Murdoch was apparently recorded telling journalists he regretted the level of cooperation over phone-hacking and illegal payments.
Labour MP Tom Watson called for police to question Mr Murdoch over the alleged comments, telling Channel 4 News:
What I would like to know is what are they sitting on that they've not given the police. And I'm sure that this transcript and this audiotape should be in the hands of the police tomorrow because I hope that they're going to be interviewing Rupert Murdoch about what he did know about criminality in his organisation ...
Rupert Murdoch told Parliament one thing and told his staff another. He told Parliament that he was fully co-operating with the police, he told his staff that it was a mistake they were co-operating with the police.
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."
Wendi Deng gained popularity for springing to her husband's aid when a protester threw a custard pie at him as he appeared before MPs to answer questions about phone hacking in 2011.
At 44, Ms Deng is 38 years younger than Mr Murdoch, who is 82.
Rupert Murdoch's divorce filing said the "relationship between husband and wife has broken down irretrievably," according to a New York Times report.
It added that a spokeswoman for News Corporation, his media company, confirmed that it was Mr Murdoch who had made the filing.
The spokeswoman added that the divorce would have no impact on the company.
Rupert Murdoch's first marriage to flight attendant Patricia Booker took place in 1956 and lasted 11 years. They had one daughter, Prudence, in 1958.
In 1967, he married the Scottish-born journalist Anna Torv after the pair met at his Sydney-based newspaper The Daily Telegraph.
They had three children together - Elisabeth, Lachlan and James - over the course of more than 30 years of marriage.
Within a month of their divorce in 1999, Murdoch married Chinese-born TV executive Wendi Deng with whom he had two more daughters - Grace and Chloe.