Apple has been gradually introducing AI features to its products, starting last year in the US.
Investors have been hoping this will re-ignite sales, which have slowed as customers hold onto their phones and other products for longer.
Mr Cook said Apple had seen a record number of purchases of new iPhones from people who already own older iPhones.
The company said overall sales rose 4% to $124.3bn, lifted by a jump in its computer sales and strong growth in its services business, which includes Apple TV, Apple News and Apple Pay.
Profits rose 7% year-on-year to $36.3bn.
