Apple's stock rose sharply Monday after chief executive Tim Cook sent a rare e-mail to a news commentator, saying sales in China had been strong.

Cook's statement was in response to an e-mail from CNBC host Jim Cramer Sunday evening inquiring about the status of Apple's business in China, its second biggest market.

"I can tell you that we have continued to experience strong growth for our business in China through July and August," Cook said in his reply to Cramer. "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."

The statement from Apple, which usually does not give mid-quarter updates, came at a time when global stock prices were tumbling amid concerns China's economy was slowing faster than analysts had expected. "At the end of the day, China is so much a big piece of global demand now that the whole market is affected," Cowen & Company analyst Timothy Arcuri told USA Today.  

After Cramer shared the e-mail to the public Monday morning, Apple's stock bounced back from a 13-percent decline, before falling again. The stock ended the day down 2.5%.

Apple's rebound helped the broader US market recover some losses from a massive selloff.

"The fact that (Cook) publicly gave some positive signs around what Apple is seeing out of China during this market meltdown is a huge sigh of relief for investors who have started to have nightmares about what China can become over the coming years for Apple," FBR analyst Daniel Ives told Reuters.

The health of Apple's business concerns many investors because of its size. Apple, the world's most valuable company, represents 3.5% of the S&P 500, and 4% of the Dow Jones. "If Apple stock falls, it drags down so many other stocks in so many portfolios because it is a part of so many portfolios," University at Buffalo finance professor Cristian Tiu told USA Today.

In the past month through Friday, Apple shares have lost more than 20% of their value, dragged down by concerns a slowing demand in China might stunt growth.

But with China's expanding middle class, Cook said he remained optimistic of Apple's long-term prospects in the world's second biggest economy.

Apple's sales growth in Greater China, which includes Hong Kong and Taiwan, has outperformed the overall performance of the company. In the latest fiscal year, its sales in the region more than doubled from just three years earlier.

As it continues to gain market share in China, Apple is expanding operations. By mid-2016, it will have increased its stores in the region to 40, if plans materialize.

Many people in China are first-time buyers of smartphones, but there are indications the market is nearing saturation.

Last week, research firm Gartner said smartphone sales in the country fell in the second quarter for the first time. China is the world's biggest market for smartphones.