The apology comes after state media including TV channel CCTV picked up an anti-Apple campaign run by Chinese consumers, describing the company as being run with "arrogance" and "greed".
A statement on Apple's China website today argued that "misunderstandings" may have led to the perception "Apple's attitude was arrogant" towards Chinese customers.
In the statement Mr Cook said the company would improve the repair policy on its iPhone 4 and iPhone 4S, and add more detailed warranty information.
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"We are aware that a lack of communications... led to the perception Apple's attitude was arrogant and that we do not care and attach importance to consumer feedback," Mr Cook wrote.
"We express our sincere apologies for any concerns or misunderstandings this gave consumers."
The company has promised to now replace defective devices covered by its one-year warranty rather than just the parts that malfunction.
The news comes at an inopportune time for Apple, as a lawsuit threatens Apple’s hold on Siri in China.