Scotland Yard detectives were on Friday attempting to track down a secret recording of Rupert Murdoch admitting to Sun journalists that payments to public officials were part of "the culture of Fleet Street".

A police officer connected to the Operation Elveden investigation into illicit payments from journalists has made a formal request to Exaro News, the investigations website that broke the story, to hand over the undercover tape.

DCI Laurence Smith told Exaro News that the police would seek a production order compelling it to disclose the recording if it did not do so voluntarily. It is understood the police have also approached Channel 4, which aired a small part of the recordings.

The development is the clearest indication yet that police in London are ready to examine Murdoch's private disclosures since the tapes emerged on Wednesday night. Murdoch is recorded saying the culture of paying police officers for stories "existed at every newspaper in Fleet Street. Long since forgotten. But absolutely."

Mark Watts, the editor-in-chief of Exaro News, said he had not handed any material to Scotland Yard and the force had not made clear "what they want, or why exactly they want it".

He said: "We are making public everything that we have, and I cannot see how else we can help. Like everyone else, they just need to keep logging on to Exaro. One thing is for certain, unlike News International, we will not – under any circumstances – betray confidential sources."

Although the 82-year-old media mogul did not admit knowing that any of his employees specifically paid public officials, he was recorded on two separate occasions describing the practice as part of the culture of Fleet Street.

On one clip published by Exaro News, an unidentified Sun journalist asks him: "I'm pretty confident that the working practices that I've seen here are ones that I've inherited, rather than instigated. Would you recognise that all this predates many of our involvement here?"

Murdoch replies: "We're talking about payments for news tips from cops. That's been going on a hundred years, absolutely. You didn't instigate it." Earlier in the tape, Murdoch tells the Sun journalists: "I don't know of anybody, or anything, that did anything that wasn't being done across Fleet Street and wasn't the culture."

News UK, formerly known as News International, has maintained that Murdoch "never knew of payments made by Sun staff to police before News Corporation disclosed that to UK authorities". Scotland Yard, meanwhile, said it would not give a "running commentary" on Operation Elveden.

The press law campaign group Hacked Off on Friday urged the Commons culture, media and sport select committee to recall Murdoch, and said he "may have committed contempt of parliament".

Evan Harris, the associate director of the group, wrote to the cross-party committee's chairman, John Whittingdale MP, saying: "There is a strong prima facie case that Mr Murdoch may have committed contempt of parliament by misleading your committee over his true response to the police investigations into phone hacking and bribery of public officials.

"As far as the victims of phone hacking are concerned, the appropriate course of action is for the committee to recall him at the earliest available opportunity to explain the discrepancies between the expressions of remorse he made to you and the defiant and unrepentant tone of his private remarks earlier this year."

The leaked recordings revealed for the first time the level of bitterness harboured by arrested Sun journalists towards News Corporation's management and standards committee (MSC), which was tasked with handing over internal documents to the police. After the first arrests in early 2012, a source close to the MSC described the operation as "draining the swamp".

In an interview published on Friday, the Sun's crime editor, Mike Sullivan, said of that phrase: "After 20 years on the paper, I admit I felt sick to my stomach at that. And I still do." Sullivan was arrested under Operation Elveden in January 2012 and cleared in April 2013.