China is Apple's second-biggest market, and its iPhones and other products - many of them made in the country - are highly popular, although it faces fierce competition from South Korea's Samsung.
State media, particularly the People's Daily, the Communist Party's mouthpiece, carried attacks on Apple over its customer service and returns policies over several days, although some users expressed support for the firm Tuesday.
In a Chinese-language letter to "respected Chinese consumers" issued on the company's website late Monday, Cook said Apple had "profoundly reflected on the opinions" expressed over its policies in the country.
"We realised that the lack of external communication during the process has led the outside world to think that Apple was arrogant and did not care or paid no attention to consumers' feedback," he said.
"We sincerely apologise for any concerns or misunderstanding this has caused to consumers."
Cook, who took over as Apple's CEO from founder Steve Jobs in August 2011, added that the firm had "many things we have to learn" in terms of operating and communicating in China and will revise some warranty policies.
Apple will provide new components, including new back covers, when replacing any parts of iPhone 4 and iPhone 4S models that break down, he said.
Chinese consumers have had to pay around US$80 for new back covers, said Chinese media reports, which said the policy amounted to "double standards" as they were free in other markets including South Korea, Britain, and Australia.
"We have always respected China in an unparalleled manner and Chinese consumers have always been our priority among priorities," Cook said in the statement.
The People's Daily ran critical items for five consecutive days last week, at one point urging consumers to "strike away Apple's unparalleled arrogance", after condemnations on state broadcaster CCTV.
Opinions split
However, users of China's Twitter-like weibos were split on Tuesday, with some backing Apple and saying state-owned Chinese firms deserved more criticism for poor service.
"CCTV can just hunt down foreign (companies). Go hunting down China Unicom and China Telecom if you really have guts," said a weibo user with the online handle Miss Aquan, referring to two state-owned telecom operators.
Liwan Langshao, another Internet user, suggested Apple had been forced into the apology, saying: "You will be the next Google if you do not bow your head."
Google in 2009 suffered state media pot shots followed by official penalties.
The US firm effectively shut down its Chinese search engine in 2010 after months of tensions with the government over censorship, and now sends mainland users to its uncensored site in Hong Kong.
Chinese state-run media generally welcomed Apple's apology on Tuesday, with the nationalist Global Times saying it showed the firm's "professionalism and flexibility" and was "worth respect".
"The blame should not only lie in foreign companies, but also China's business environment," it said in an editorial in its English-language edition, with a largely similar version printed in Chinese.
An Apple representative declined to comment further on the letter Tuesday, saying: "Tim's letter (has) a lot of information there and that is our official statement."
Source: AFP, via I-Net Bridge
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