Apple’s business is being tested by ongoing weakening of its iPhone sales.
That lifted quarterly revenue to $64bn (£49.6bn), up 2% year-on-year.
Mr Cook has been working to make Apple’s business less reliant on its phones, with new subscription services for news and television, among other offerings, but iPhones still account for a majority of sales.
Mr Cook said his optimism about the iPhone 11’s appeal is reflected in Apple’s relatively bright forecast for the upcoming quarter, which includes the festive season – typically a time that sees many hardware purchases.
The firm said it expected revenue growth in the quarter of as much as 6%, above analysts’ expectations.
Daniel Ives, analyst at Wedbush Securities, said Apple also impressed investors with the resilience of its performance in its Greater China region, which accounts for nearly 20% of its business. Sales there declined less than 3%.
On a call with investors, Mr Cook predicted additional growth in the region and expressed confidence that the US and China would reach an agreement that would avoid additional tariffs.
“The tone, I think, has changed significantly,” he said.
Apple shares gained almost 2% in after-hours trade.