The News International-owned tabloid published its final issue last Sunday after being hit with reports that journalists on the paper had hacked into the voicemail messages of missing schoolgirl Milly Dowler, families of victims of the 7/7 London terrorist attacks and of relatives of UK soldiers killed in combat.
In an interview with The Wall Street Journal, also owned by News Corporation, Murdoch addressed the closure of the newspaper less than a week after the new claims surfaced, saying: "We think it's important to absolutely establish our integrity in the eyes of the public... I felt that it's best just to be as transparent as possible.
"When I hear something going wrong, I insist on it being put right."
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Murdoch also defended son and chief executive of News Corporation International James against criticism that he was slow in dealing with the allegations, adding: "I think he acted as fast as he could, the moment he could."
The media mogul also denied suggestions that the scandal had both eliminated his chances of buying the 61% of Sky that he does not own and tarnished the image of News Corporation, saying that the damage to his company is "nothing that will not be recovered".
It was reported earlier that Murdoch has agreed to appear in front of the judge-led inquiry into phone hacking, after he turned down a request to answer questions from the Commons Culture, Media and Sport Committee on July 19.
Former News of the World editor and News International chief executive Rebekah Brooks has however confirmed that she will appear before the Committee next Tuesday.