"As you know, we don't give mid-quarter updates and we rarely comment on moves in Apple stock," Cook wrote. "But I know your question is on the minds of many investors."
"I get updates on our performance in China every day, including this morning, and I can tell you that we have continued to experience strong growth for our business in China through July and August. Growth in iPhone activations has actually accelerated over the past few weeks, and we have had the best performance of the year for the App Store in China during the last 2 weeks."
"Obviously I can't predict the future, but our performance so far this quarter is reassuring. Additionally, I continue to believe that China represents an unprecedented opportunity over the long term as LTE penetration is very low and most importantly the growth of the middle class over the next several years will be huge," Cook added.
Apple shares traded down more than 5 percent in pre-market trading.
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—CNBC's Jim Cramer contributed to this report.