This follows a prior post in which John Legend denounced The New York Post publically for running the "cartoon" in question.
In a statement published in the newspaper on Tuesday, Murdoch said he wanted to "personally apologise to any reader who felt offended, and even insulted" and admitted that the cartoon had been a "mistake".
The newspaper had previously issued a partial apology in an editorial, but slammed "opportunists" in the media and public life who they claimed took advantage of the furore to seek "payback".
After explaining that the cartoon had been misinterpreted, the editorial, published last Thursday, concluded: "Sometimes a cartoon is just a cartoon - even as the opportunists seek to make it something else."
The controversial cartoon depicted police officers shooting dead a chimpanzee - a reference to a real-life incident last week when a pet simian was killed after it mauled a woman in Connecticut.
"They'll have to find someone else to write the next stimulus bill," observed an officer with a smoking gun in the image.
The country's first African-American president had the previous day signed the $787 billion economic recovery bill after a heated debate in Washington. Rev Al Sharpton, the prominent civil rights activist, immediately accused the newspaper, which has a conservative editorial tone, of deploying a crude racist stereotype of blacks as monkeys.
Col Allan, the Post's editor-in-chief, had vigorously defended the cartoon as a parody of Washington politics, saying it "broadly mocks Washington's efforts to revive the economy".
But his defence did little to defuse the anger of critics, and the blogosphere was filled with condemnation for the paper.
"Last week we made a mistake," wrote Murdoch, head of the media giant News Corporation, which owns the Post.
"I have had conversations with Post editors about the situation and I can assure you - without a doubt - that the only intent of that cartoon was to mock a badly written piece of legislation.
"It was not meant to be racist, but unfortunately, it was interpreted by many as such."
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Emily Holleman
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Comments
I think understanding what will happen in the future is important for two reasons. One is to understand that there is something in place to help avoid it in the future, but the other is counterbalancing: to make sure the instructions on what to avoid in the future are not overly broad, creating some era of censorship that goes too far the other way.
I personally tend to believe there's a serious possibility that this was a well-intentioned cartoon that had an unfortunate misreading. Yet even in my view, I think it's a good idea that the Editors be more sensitized to the misunderstandings that can arise.
On the other hand, while I'm all for watching out for tastefulness and danger, at the same time I want a robust public dialog. We lost the show Politically Incorrect over ABC getting similar pressure after a single remark by Bill Maher that struck people the wrong way. That show was a critical outlet for important views that did not otherwise have an airing. We're just lucky as a public that HBO picked him back up because we need the voices that appear on Bill's shows, even at the sometimes risk of provoking problems.
Political commentary risks offending people and is quite a tricky business; if you get it reliably right, I bet that means you're erring on the side of being too cautious, and hence not making some essential points.