Apple Inc.'s China business experienced "strong growth" in July and August, chief executive Tim Cook told CNBC on Monday, seeking to assuage investor concerns over the company's prospects in a market considered critical for its growth.

IPhone activations in China had accelerated over the past few weeks and the App Store in China had its best performance of the year over the past two weeks, Cook told CNBC in an emailed response to questions about Apple's business in China.

A slump in China's stock market, slowing economic growth and Beijing's move last week to devalue the yuan have added to Apple's investors' concerns about rising competition from local rivals Xiaomi Inc and Huawei Technologies Co. Apple gets over a quarter of its sales from China.

Apple's shares slumped as much as 13 percent to a year-low of $92 in early trading on Monday, amid a sell-off in the broader U.S. market.

The shares recovered to trade down 1.6 percent at $104.02 as the market pared some losses and investor's took note of Cook's comments.

"Obviously I can't predict the future, but our performance so far this quarter is reassuring. Additionally, I continue to believe China represents an unprecedented opportunity over the long term ... ," Cook said in the email.

Cowen and Co. analyst Timothy Arcuri thinks Apple is likely see the impact of the China slowdown only over the next few months.

"I am concerned about a slowdown in Apple's demand from China and I think they haven't even seen the extent of it yet," said Arcuri.

The concerns over China were exacerbated last week after a Gartner report said smartphone sales in the country fell for the first time ever in the previous quarter.

China's smartphone market is widely believed to be close to saturation with fewer first-time buyers.

FBN Securities analyst Shebly Seyrafi said factors such as disappointing iPad sales and demand for Apple Watch have also weighed on Apple.

Verizon's recent move to stop smartphone subsidies and ask customers to buy phone though a contract was also a concern, Seyrafi said.