By Lorraine Luk

Apple Inc. is preparing for its largest initial production run of iPhones, betting that larger-screen models will lure consumers now attracted to similar phones from Samsung Electronics Co. and others.

The Cupertino, Calif., company is asking suppliers to manufacture between 70 million and 80 million units combined of two large-screen iPhones with 4.7-inch and 5.5-inch displays by Dec. 30, according to people familiar with the matter.

Its forecast for what is commonly called the iPhone 6 is significantly larger than the initial order last year of between 50 million and 60 million versions of the iPhone 5S and 5C–which had a display measuring 4-inches diagonally, these people said. Both of the coming models are expected to feature metal cases similar to the iPhone 5S and likely come in multiple colors, these people said.

Apple stuck with smaller displays on iPhones even as rival smartphone makers rolled out bigger screens and customers clamored for larger phones. Demand for larger-screen smartphones boosted Samsung, which started offering a 4.8-inch display in its Samsung Galaxy S models in 2012 and introduced an array of bigger phones.

Apple is scheduled to report its fiscal third-quarter results on Tuesday and provide a financial outlook for the current period ending Sept. 28. Historically, Apple has released a new iPhone in mid-September.

Analysts are forecasting Apple will report sales of about 35.9 million iPhone units for the three months ended June 30. That would be up about 15% from a year earlier.

For Apple, one possible hiccup with the larger screen is that display makers for the new iPhones are struggling to improve the production of the larger 5.5-inch screens, people familiar with the matter said. The production is complicated because the displays are using in-cell technology, which allows the screens to be thinner and lighter by integrating touch sensors into the liquid crystal display and making it unnecessary to have a separate touch-screen layer.

To factor in the possibility of a higher failure rate for displays, Apple has asked component makers to prepare for up to 120 million iPhones by year-end, the people familiar with the matter said. It made a similar request last year to prepare enough parts for a combined 90 million iPhones to provide some slack in its supply chain.

The 5.5-inch iPhone screen would face an additional manufacturing complication if it uses a cover using sapphire crystal, a more durable but costly alternative to glass, people familiar with the matter said.

Apple’s iPhone production forecast assumes a surge in demand from Apple’s partnership with China Mobile Ltd., the world’s largest carrier, which started offering the iPhone earlier this year. Bigger-screen smartphones are also popular in China and other emerging markets where the smartphone is replacing the personal computer as a main computing device.

As Apple competes against Google Inc.’s Android operating system, larger screens are now common in Apple’s core mobile market–high-price phones. In May, 98% of Android smartphones that sold globally at the equivalent of $400 or above featured a display greater than 5 inches, according to Counterpoint Research.

The new iPhones are coming to market as Samsung’s smartphone business is showing signs of sluggishness. Earlier this month, Samsung warned that its earnings would fall for a third straight quarter due to a glut of unsold smartphones. It is feeling the pinch in emerging markets where its low- to mid-end smartphones are facing intense price competition from rival Asian handset makers including Lenovo Group Ltd. and Xiaomi Inc.

Every year, Apple faces a delicate balancing act. It is critical for Apple to ensure that it has enough supplies of a new iPhone during the holiday season when demand is greatest. Shortages can often result in sales for its rivals, although too much inventory also is a concern.

Apple disappointed investors in last year’s December quarter when iPhone sales rose 7% from a year earlier, falling short of Wall Street expectations of a 15% increase as it struggled to fulfill demand for the 5S and failed to move enough 5C units. The slump proved temporary, with Apple reporting a 17% increase in the following quarter.

Michael Walkley, an analyst at Canaccord Genuity, said there is “strong pent-up demand” for the iPhone 6 because customers have held off on upgrading from older iPhone models.

To fulfill Apple’s demands, the company’s two main iPhone assemblers— Pegatron Corp. and Hon Hai Precision Industry Co., also known as Foxconn–are on a hiring binge at their respective manufacturing sites in China. Foxconn, for example, is hiring workers by the hundreds a day to staff production lines at their respective manufacturing sites in China, said people familiar with those companies.

Foxconn and Pegatron plan to start mass producing the 4.7-inch iPhone model next month and Hon Hai will begin making the 5.5-inch version exclusively in September, the people said.

Often, Apple’s production forecasts are adjusted based on early demand, according to people familiar with the matter. For example, Apple tweaked its initial forecasts for the iPhone 5S and iPhone 5C last year when the more expensive 5S initially sold better than expected and the 5C slumped in the first few months, these people said.

Apple Chief Executive Tim Cook has also warned that the supply chain is “very complex” and that it is impossible to take a data point from a supplier and extrapolate a broader meaning for Apple’s business.

Suppliers also say that Apple likes to build up inventory heading into the new year, because it is difficult to keep production lines humming at full capacity since many workers go home during Lunar New Year, which is in February next year.

Write to Lorraine Luk at lorraine.luk@wsj.com, Daisuke Wakabayashi at Daisuke.Wakabayashi@wsj.com and Eva Dou at eva.dou@wsj.com