Rupert Murdoch has been asked to explain to MPs his comments about the "totally incompetent" police investigation into allegations of phone hacking and corrupt payments.

The News Corp boss was apparently recorded describing the treatment of journalists who had been arrested as a disgrace and saying police had been told to obtain court orders to get information, rather than the company offering up material as it had done previously.

Home Affairs Select Committee chairman Keith Vaz has written to Mr Murdoch asking him to comment on the secret recording.

The request follows evidence to the committee from the Metropolitan Police's assistant commissioner Cressida Dick, who said that since May voluntary co-operation had been significantly reduced.

She also said Scotland Yard was trying to obtain a copy of the recording of Mr Murdoch.

On the secret tape, Mr Murdoch is heard railing at the way the police behaved. "Still, I mean, it's a disgrace. Here we are, two years later, and the cops are totally incompetent," he said.

"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.

"But why are the police behaving in this way? It's the biggest inquiry ever, over next to nothing."

When a journalist asked why so much material had been handed over, Mr Murdoch indicated he believed it had gone too far.

"Because – it was a mistake, I think," he said. "But, in that atmosphere, at that time, we said, 'Look, we are an open book, we will show you everything'. And the lawyers just got rich going through millions of emails."

Mr Murdoch is also expected to be recalled by the Culture, Media and Sport select committee in the autumn to answer questions about the tape.