Apple's smartphone revenue came in at a record US$61.58 billion for the quarter ending 30 December, a rise of 13% on the corresponding quarter a year prior.
But the number of iPhones sold fell by 1% to 77.3 million units, the company said.
The firm's total revenue was US$88.29 billion, up 13% over the corresponding quarter a year ago. Of this, 65% came from international sales. Profits went up by 12% to US$20.07 billion.
The company's smartwatch division and wireless earbuds also experienced strong sales.
Apple has projected second-quarter revenue below analysts' expectations of US$66.54 billion, saying it would range from US$60 billion to US$62 billion. This forecast represents a rise from the corresponding quarter a year ago.
Analysts' predictions had been higher but in recent weeks there have been reports of a cut in iPhone X production by half in the first three months of 2018, leading to a moderation in predicted figures.
“We’re thrilled to report the biggest quarter in Apple’s history, with broad-based growth that included the highest revenue ever from a new iPhone line-up. iPhone X surpassed our expectations and has been our top-selling iPhone every week since it shipped in November,” said Apple chief executive Tim Cook.
“We’ve also achieved a significant milestone with our active installed base of devices reaching 1.3 billion in January. That’s an increase of 30% in just two years, which is a testament to the popularity of our products and the loyalty and satisfaction of our customers.”
Apple chief financial officer Luca Maestri said: “Thanks to great operational and business performance, we achieved all-time record profitability during the quarter, with EPS up 16%.
“Cash flow from operations was very strong at US$28.3 billion, and we returned US$14.5 billion to investors through our capital return programme.”