Apple's business is being tested by ongoing weakening of its iPhone sales.
In the most recent quarter, iPhone sales dropped to $33.4bn (£25.9bn), down almost 10% year-on-year.
The fall extended a streak of declines and hit the firm's profits in the quarter, which slipped about 3% year-on-year to $13.7bn.
The firm's profit and revenue for the full financial year also fell for the first time since 2016, weighed down by the iPhone results.
In a presentation after the firm released its earnings, Apple boss Tim Cook hastened to reassure investors that the declines in iPhone sales are slowing, thanks to the popularity of the firm's latest model, the iPhone 11.
"It's early but the trends look very good," he said. "We are bullish."
Mr Cook added that the firm's other businesses were healthy - sales of wearables, such as earphones and watches, surged by more than 50%, while services revenue, which includes Apple Pay and the app store, jumped 18% year-on-year.
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.