Cook responded to a query from CNBC about the sharp drop in Apple shares amid the market upheaval in China and around the world.
"As you know, we don't give mid-quarter updates and we rarely comment on moves in Apple stock. But I know your question is on the minds of many investors," Cook wrote to CNBC's Jim Cramer in an email released by the cable channel.
Cook noted that he gets updates daily on Apple activity in China "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."
He said that "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 two weeks."
Cook added: "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 of Friday, Apple stock has slumped more that 20 percent from its peak earlier this year at USD 133.
Apple shares fell as much as 12 per cent in morning trade, but then swung back to positive territory, and were up 2.1 per cent at USD 108 shortly after 1700 GMT.