Apple returned to increasing revenue in the holiday quarter and said the growth rate could accelerate in the coming months, as iPhone sales rebounded strongly in the North America, Western Europe and Japan.

However, despite forecasting revenues to grow as much as 6 per cent in the current quarter, its outlook fell just short of Wall Street’s estimates amid continuing sales declines in China and foreign currency headwinds.

Apple sold 78.3m iPhones in the quarter ending in December, up 5 per cent year-on-year and better than most analysts expected. Total revenues were up 3 per cent to $78.4bn, a new all-time high for Apple and exceeding both its own and Wall Street’s forecasts. Earnings grew 2.4 per cent to $3.36 per share, while net income fell by 2.6 per cent to $17.9bn.

“We sold more iPhones than ever before and set all-time revenue records for iPhone, Services, Mac and Apple Watch,” said Tim Cook, Apple’s chief executive, in a statement. “Revenue from Services grew strongly over last year, led by record customer activity on the App Store, and we are very excited about the products in our pipeline.”

For the quarter ending in March, Apple said revenues would be between $51.5-53.5bn, compared with Wall Street’s consensus estimates of $54bn, while gross margin was in-line with analysts’ forecasts at 38-39 per cent.

The tech heavyweight’s shares jumped about 3 per cent in after-hours trading.

In an interview, Apple’s finance chief, Luca Maestri, said that the iPhone saw “double digit unit growth” in the US, Canada, all of Western Europe, Japan and Australia. While overall sales in Greater China, which includes Hong Kong, fell by 12 per cent. Mr Maestri said Apple was “​happy​ ​with​ ​the​ ​result” given the rate of decline has moderated from the second half of last year. In mainland​ China,​ ​revenue​ ​was​ ​flat​ ​year-on-year ​and​ ​up​ ​in​ ​constant​ ​currency​ ​terms, he added.

The popularity of the iPhone 7 Plus boosted the smartphone’s average selling price to $694 in the last quarter, even though supplies were outstripped by demand until this month.

“We were a bit surprised by the mix of the 7 Plus,” Mr Maestri said. “We could have sold more.”

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