SAN FRANCISCO — Apple’s growth prospects are looking brighter as anticipation builds for the upcoming release of the next iPhone, a model that is expected to cater to consumers yearning for a bigger screen.

The latest evidence of Apple’s mounting momentum emerged Tuesday with the release of the company’s third-quarter report.

Earnings rose at the highest rate in nearly two years as Apple Inc. sold 35.2 million iPhones during the period. The iPhone shipments climbed 13 percent from the same time last year, even though many people are believed to be holding off on purchases until the next version comes out this fall.

“From an execution perspective, we did a really great job,” Apple Chief Financial Officer Luca Maestri told The Associated Press. “We have some things in the pipeline that we think people will really be excited about.”

Apple earned $7.7 billion, or $1.28 per share, for the three months ending June 28. That represented a 12 percent increase from income of $6.9 billion, or $1.07 per share, at the same time last year. It’s the first time that Apple’s earnings have increased by more than 10 percent since the quarter that included the September 2012 release of the iPhone 5 – the last time that the company boosted the device’s screen size.

The earnings for the latest quarter exceeded the average estimate of $1.23 per share among analysts surveyed by FactSet.

Revenue rose 6 percent from last year to $37.4 billion – $600 million below analysts’ forecasts.

If media reports based on leaks from Apple suppliers prove accurate, the iPhone 6 will boast a screen of at least 4.7 inches compared to the current 4-inch display. Some analysts also speculate Apple will also unveil an iPhone with a 5.5-inch screen.

An iPhone with a larger screen probably would unleash a flood of sales. A bigger-screen iPhone might also tempt consumers already accustomed to the larger screens on a variety of smartphones running on Google Inc.’s Android operating system.

Apple is also believed to be gearing up to release a smartwatch, a move that would mark the first time the company has entered a new device market since Tim Cook replaced the late Steve Jobs as CEO nearly three years ago.

The chances of Apple unveiling a high-tech watch as a complement to the iPhone looked even more likely Tuesday when Apple was granted a U.S. patent for a touch-screen device designed to be worn on wrists. Sketches attached to the filing with the U.S. Patent and Trademark Office indicated that Apple intends to call the device, “iTime.”

The iPhone’s third-quarter sales growth was strongest in Brazil, India, Russia and China, where device sales increased 55 percent from last year. The gains are testament to the ongoing allure of Apple’s marquee product seven years after the first iPhone came out.

Apple’s trend-setting tablet computer, the iPad, seems to be losing its appeal amid a bevy of cheaper alternatives. The Cupertino, California, company shipped 13.3 million iPads in the latest quarter, a 9 percent drop from the same time last year.

Apple is counting on a new partnership forged with IBM Corp. to help boost iPad sales to corporate customers and government agencies.

Propelled by hopes for the next iPhone and the potential release of a smartwatch, Apple’s stock has surged 18 percent this year. After closing at $94.72 Tuesday, the stock is just $6.01, or about 6 percent, away from setting a new high.