The Australian-born 82-year-old last appeared before parliament's Culture, Media and Sport Committee two years ago at the height of the hacking scandal that closed the News of the World tabloid.
A spokeswoman for the scrutiny panel confirmed that it would ask Murdoch to appear again to discuss his comments on the police probe, adding that it was expected to happen in the autumn although no date has been agreed.
According to the tape obtained by the Exaro investigative website and released by Channel 4 television last week, Murdoch said his US-based News Corporation made a "mistake" in handing over so much information to police.
Murdoch was speaking in March at a meeting with journalists at his top-selling British tabloid The Sun, where he also appears to suggest that reporters jailed as a result of the probe could return to their jobs.
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Murdoch shut down his top-selling News of the World tabloid in July 2011 after it emerged the weekly had illegally accessed the voicemails of hundreds of public figures, including a murdered teenager.
In his first appearance before the committee later that same month, alongside his son James, Rupert Murdoch apologised and said "this is the most humble day of my life".
The committee published a scathing report in May 2012 saying Murdoch was unfit to lead a major global company.