In a Chinese-language statement to "respected Chinese consumers" issued on the company's China website, Mr Cook said "misunderstandings" may have led to the perception "Apple's attitude was arrogant" towards Chinese customers.
He promised to improve the repair policy on the iPhone 4 and iPhone 4S, and to improve warranty information.
"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," Mr Cook, who took over from founder Steve Jobs in August 2011, said. "We express our sincere apologies for any concerns or misunderstandings this gave consumers."
Chinese state media, particularly the state's flagship newspaper People's Daily, have carried a series of attacks on Apple over its customer service and returns policies.
China is Apple's second-biggest market and earlier this year Mr Cook said he expected it to replace North America as Apple's largest source of revenue.
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