Mr Murdoch said the paper had made a mistake in printing the cartoon
The owner of the New York Post, Rupert Murdoch, has apologised for a cartoon which critics said was a racist depiction of President Barack Obama.
Newspaper cartoonist Sean Delonas drew police shooting dead a chimp, while remarking "they'll have to find someone else to write the stimulus bill".
But Mr Murdoch said the cartoon was meant to mock Mr Obama's legislation and was not intended to be racist.
The newspaper had apologised to readers last week after widespread criticism.
The cartoon, published on 18 February, came a day after Mr Obama signed into law a $787bn (£548bn) economic stimulus package approved by Congress after weeks of wrangling.
The image referred to a gruesome incident earlier that week, when a pet chimp in Connecticut attacked and disfigured a woman before being shot dead by police.
In an editorial in Friday's edition, Mr Murdoch said the paper had made a mistake in publishing the cartoon and that he was sorry for any offence.
"As the Chairman of the New York Post, I am ultimately responsible for what is printed in its pages. The buck stops with me."
The cartoon brought criticism from anti-racism campaigners
"Last week, we made a mistake. We ran a cartoon that offended many people. Today I want to personally apologize to any reader who felt offended, and even insulted."
He said he had spoken to a number of people since the publication and that he could now "better understand the hurt this cartoon has caused".
But he added 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."
Mr Murdoch said the New York Post would "seek to be more attuned to the sensitivities of our community" in the future.
Commentators, blog writers and politicians had widely denounced the cartoon and demonstrators picketed the newspaper's New York City headquarters.
Mr Delonas had denied that the chimp resembled Mr Obama, and the paper initially defended the cartoon as a "parody of a current news event" but later apologised.