A prominent Labour MP has said US authorities should press corporate corruption charges against Rupert Murdoch's global empire after he admitted in a secretly recorded meeting with staff on the Sun that payments to police were part of "the culture of Fleet Street".

Chris Bryant, who has been compensated for phone hacking by the defunct News of the World, said the latest revelations were "another reason" for the FBI to take action under the foreign corrupt practices act, which makes it an offence for American companies to pay public officials on foreign soil.

The MP for Rhondda said he had spoken to the Met police, and claimed the force had been in touch with the FBI. But he added that he believed the UK authorities were reluctant to consider bringing any corporate corruption charges in the UK because the force was "waiting for Operation Elveden [the investigation into unlawful payments made to public officials] to finish".

Meanwhile, Labour colleague Tom Watson, MP for West Bromwich East, has written to a leading US politician, Senator John D Rockefeller, asking him to ensure the US authorities' investigations into News Corporation "are not inhibited in going to the very top".

The latest scandal over alleged payments to police erupted after Sun journalists secretly taped a 45-minute meeting in March between Murdoch and at least 24 staff who had been arrested in relation to Scotland Yard's Elveden investigation.

Although Murdoch does not admit to knowing that any of his employees specifically paid officials, he is recorded as saying the culture of paying public officials for stories "existed at every newspaper in Fleet Street. Long since forgotten. But absolutely." Murdoch says he first knew about the Prevention of Corruption Act 1906, which until recently made it a crime to pay police and other public officials, a few weeks before his meeting with staff. The act has since been superseded by the Bribery Act 2010.

On the recording, one unidentified member of staff interjects: "So, completely oblivious to the fact that the long-term practice of this company to pay public officials was illegal, my job description meant that as a result of that, it came directly through my particular department. You can understand how we all feel that we are effectively being made scapegoats."

The News Corporation chief executive replies: "Yeah. And one of these high-priced lawyers would say it's our fault, but that situation existed at every newspaper in Fleet Street. Long since forgotten. But absolutely. It was the culture of Fleet Street."

But then the media mogul appears to admit he knew it was common practice.

A 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 says: "We're talking about payments for news tips from cops. That's been going on a hundred years, absolutely. You didn't instigate it."

Bryant believes this is enough for the US authorities to act: "American law is much tougher than UK law: you don't have to prove that a director knew it. The mere fact that a company engaged in paying public officials is enough to bring a body corporate charge … the charge can be brought because the directors did not have a governance system in place to stop it."

He said he had been told by the Met that they had been in talks with the FBI.

Mark Lewis, the lawyer representing the Dowler family and other phone-hacking victims, said Murdoch's private remarks would be held up by lawyers in the US where a number of civil claims are being prepared over phone hacking under various US acts, including the stored communications act and the wiretap act.

He said: "No doubt the FBI will be very interested in comments that suggest a senior director of a company was fully aware of payments to foreign officials. As far as the US claims are concerned, this raises further evidence of knowledge at the highest levels of News Corp of unlawful activities."

Journalists connected with the tabloid have told the Guardian they were shocked to find out that the police had been given notes taken in private conversations with a law firm, Linklaters, which had been brought in as an adviser to the management and standards committee in July 2011.

Several senior journalists were asked to talk to Linklaters on the basis that the law firm needed help in understanding how newspapers worked. "We were given letters telling us that this was a good thing to do, that there was nothing to worry about," said one source.

"The meetings took several hours and the journalists were then asked to sign a statement saying that the notes taken by the lawyers were an accurate account of the conversation. They were never told the statement would be used by police. This is an utter betrayal by the company at every level," the person added.

Murdoch was tackled about the issue in the meeting in which a Sun journalist is heard saying: "Quite a number of us in this room were selected for an interview with Linklaters, the lawyers, long before any suggestion there would be arrests or there had been any wrongdoing.

"The interviews were conducted on the basis that Linklaters just wanted to get a feel for how the newspaper was put together, who did what, how it worked, all the rest of it. And then, not surprisingly now, nearly every single person interviewed by Linklaters found themselves arrested. And, indeed, large chunks of the interviews we gave to Linklaters was produced to us in the police station on our arrest."

Linklaters declined to comment.A spokesman for News UK, home to Murdoch's UK newspaper business, said: "Mr Murdoch never knew of payments made by Sun staff to police before News Corporation disclosed that to UK authorities. Furthermore, he never said he knew of payments. It's absolutely false to suggest otherwise."