SAN FRANCISCO — Apple Inc. reported quarterly iPhone sales that trailed analysts’ estimates, even after debuting new models for the holiday shopping season.
Profit was $13.1 billion, or $14.50 a share, for the quarter ended Dec. 28, little changed from $13.1 billion, or $13.81 a share, a year earlier, Apple said Monday.
Sales rose 5.7 percent to $57.6 billion.
Analysts had predicted profit of $14.07 a share on sales of $57.5 billion, according to the average of estimates compiled by Bloomberg.
The holiday results indicate that demand may be ebbing for new iPhone models — Apple’s primary source of revenue — as competitors crowd in with new smartphone and tablet offerings. The numbers are highly anticipated by Apple’s investors because the end-of-year shopping season is usually the company’s most lucrative period. Apple said it sold 51 million iPhones, falling short of analysts’ estimates of 54.7 million.
‘‘There’s a perception problem that they aren’t innovating,’’ said Brian Blair, an analyst at Wedge Partners in New York. ‘‘That’s why new product announcements will be so critical this year.’’
Chief executive Tim Cook is under pressure to boost financial results that have stagnated without the introduction of an entirely new product since the iPad’s debut in 2010. In its last fiscal year, the company posted its first annual profit decline in at least a decade.
Apple shares rose just 5.4 percent last year, trailing the Standard & Poor’s 500 index’s 30 percent gain.
Apple fell as much as 6.4 percent in extended trading after the results were released. The shares had increased less than 1 percent to $550.50 at the close in New York. While the stock is down 1.9 percent so far this year, the shares are up 26 percent in the past six months.
Apple also gave a glimpse of how sales are faring after the release earlier this month of the iPhone on China Mobile, the world’s largest wireless carrier. The company said sales will be $42 billion to $44 billion in the current quarter, with gross margins of 37 to 38 percent. Analysts had predicted sales of $46.1 billion and a margin of 37.3 percent.
Sales last quarter were fueled by the iPhone 5s and 5c, as well as the iPad Air and iPad Mini, which all made their entrances in time for the holiday rush. Apple sold 26 million iPads, compared with analysts’ estimates for 25 million units.
The company also declared a cash dividend of $3.05 a share. Apple has been pressured to return more money to shareholders. Billionaire activist investor Carl Icahn last week increased his stake in the company to about $3.6 billion and has been pressing Cook to increase the buyback program to boost Apple’s stock price. Icahn’s proposal is slated to be considered at the company’s annual shareholder meeting next month.