The once-hot smartphone market in China is expected to cool this year, growing a meager 1.2 percent, according to a report released Tuesday.

The China smartphone market grew 19.7 percent last year and accounted for nearly a third of all new handsets shipped, according to the International Data Corporation's Worldwide Quarterly Mobile Phone Tracker report.

"China clearly remains a very important market," said IDC program director Ryan Reith.

"However, the focus will be more on exports than consumption as domestic growth slows significantly."

The forecast came a day after Apple chief executive Tim Cook said that the California-based company is still seeing "strong growth" in China despite a recent global stock market downturn.

"Obviously I can't predict the future, but our performance so far this quarter is reassuring," Cook wrote to CNBC's Jim Cramer in an email released by the cable channel.

"Additionally, I continue to believe that China represents an unprecedented opportunity over the long term."

IDC trimmed its forecast slightly for the total number of smartphones it expects to be shipped worldwide this year, placing that growth at 10.4 percent, or 1.44 billion units.

Regions with the largest potential for growth in smartphone sales are price sensitive, meaning iPhones are not likely to wrest market share from lower-cost handsets powered by Google-backed Android software, according to IDC.

IDC forecast that shipments of Android smartphones would grow from 1.16 billion this year to 1.54 billion in 2019, while iPhone shipments were expected to grow from 223.7 million to 269.6 million during that same time period.

It also predicted that Android would hold on to its 81 percent share of the smartphone market.

"India has captured a lot of the attention that China previously received and it's now the market with the most potential upside," Reith said.

"The interesting thing to watch will be the possibility of manufacturing moving from China and Vietnam over to India."